Dr. Çağın KAMIŞCIOĞLU

(1)

(FZM 114) FİZİK -II

Dr. Çağın KAMIŞCIOĞLU

1

(2)

İÇERİK

+ MANYETIK ALAN

+ OERSTED DENEYI

+ SAG EL KURALI

+ AKIM TASIYAN BIR TELIN MANYETIK ALANDA HAREKETI

+ ÖRNEK

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 2

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MANYETİK ALAN

Herhangi bir duran ya da hareket eden yüklü parçacığın etrafını bir elektrik alan sarmaktadır. Herhangi bir hareketli elektrik yükünün çevresindeki uzay bölgesi elektrik alana ek olarak bir de manyetik alan içerir. Herhangi bir manyetik maddeyi de saran bir manyetik alan vardır.

Tarihsel olarak, bir manyetik alanı temsil etmek için B harfi kullanılmaktadır.

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 3

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MANYETİK KUVVET

908 C H A P T E R 2 9 Magnetic Fields

• The magnetic force exerted on a positive charge is in the direction opposite the direction of the magnetic force exerted on a negative charge moving in the same direction (Fig. 29.3b).

• The magnitude of the magnetic force exerted on the moving particle is propor- tional to sin ! _{, where} ! is the angle the particle’s velocity vector makes with the direction of B.

We can summarize these observations by writing the magnetic force in the

form (29.1)

where the direction of F _B is in the direction of if q is positive, which by definition of the cross product (see Section 11.2) is perpendicular to both v and B.

We can regard this equation as an operational definition of the magnetic field at some point in space. That is, the magnetic field is defined in terms of the force acting on a moving charged particle.

Figure 29.4 reviews the right-hand rule for determining the direction of the cross product You point the four fingers of your right hand along the direction of v with the palm facing B and curl them toward B. The extended thumb, which is at a right angle to the fingers, points in the direction of v ! B. Because

v ! B.

v ! B F _B " q v ! B

(b)

–

B

F _B

v

(a)

+

F _B

B

v

θ θ

Figure 29.4 The right-hand rule for determining the direction of the

magnetic force acting

on a particle with charge q moving

with a velocity v in a magnetic field B.

The direction of is the direc-

tion in which the thumb points. (a) If q is positive, F _B is upward. (b) If q is

negative, F _B is downward, antiparallel to the direction in which the thumb points.

v ! B

F _B " q v ! B

The blue-white arc in this photograph indi- cates the circular path followed by an electron beam moving in a magnetic field. The vessel contains gas at very low pressure, and the beam is made visible as the electrons

collide with the gas atoms, which then emit visible light. The magnetic field is pro-

duced by two coils (not shown). The appa- ratus can be used to measure the ratio e/m _e for the electron.

B manyetik alanında hareket eden yüklü parçacığa etki eden kuvvet (vektör)

Parçacığın yükü

(sayisal)

Parçacığın hızı (vektör)

Manyetik

Alan (vektör)

Bu hesaplama arkadaşlara vektörel bir özellik göstermektedir.

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 4

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OERSTED DENEYİ

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 5

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AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

Tek yüklü bir parçacık, bir manyetik alandan geçerken bir kuvvet etkisinde kaliyorsa üzerinden akım geçen bir tele de manyetik alan içinde kuvvet etkimesi süpriz değildir.

Biliyoruz ki akım zaten çok sayıda yüklü parçacıktan oluşmanktadır. Bu yüzden her bir yüklü parçacığa bir kuvvet uygulanacak ve bu kuvvetlerin toplamı tele etkiyen net kuvveti verecektir.

29.2 Magnetic Force Acting on a Current-Carrying Conductor 911

lustrations, such as in Figure 29.6b to d, we depict a magnetic field directed into the page with blue crosses, which represent the tails of arrows shot perpendicularly and away from you. In this case, we call the field B

_in

, where the subscript “in” indi- cates “into the page.” If B is perpendicular and directed out of the page, we use a series of blue dots, which represent the tips of arrows coming toward you (see Fig.

P29.56). In this case, we call the field B

_out

. If B lies in the plane of the page, we use a series of blue field lines with arrowheads, as shown in Figure 29.8.

One can demonstrate the magnetic force acting on a current-carrying conductor by hanging a wire between the poles of a magnet, as shown in Figure 29.6a. For ease in visualization, part of the horseshoe magnet in part (a) is removed to show the end face of the south pole in parts (b), (c), and (d) of Figure 29.6. The magnetic field is directed into the page and covers the region within the shaded cir- cles. When the current in the wire is zero, the wire remains vertical, as shown in Figure 29.6b. However, when a current directed upward flows in the wire, as shown in Figure 29.6c, the wire deflects to the left. If we reverse the current, as shown in Figure 29.6d, the wire deflects to the right.

Let us quantify this discussion by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure 29.7. The magnetic force exerted on a charge q moving with a drift velocity v

_d

is To find the total force acting on the wire, we multiply the force exerted on one charge by the number of charges in the segment. Because the volume of the segment is AL, the number of charges in the segment is nAL, where n is the number of charges per unit volume. Hence, the total magnetic force on the wire of length L is

We can write this expression in a more convenient form by noting that, from Equa- tion 27.4, the current in the wire is Therefore,

(29.3) F

_B

! I L ! B

I ! nqv

_d

A. F

_B

! (q v

_d

! B)nAL q v

_d

! q B v

_d

! B.

(b) B

_in

× ×

I = 0

B

_in

× ×

I

B

_in

× ×

I

(c) (d)

(a)

Figure 29.6 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field (blue crosses) is directed into the page. When there is no current in the wire, it remains vertical.

(c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

L

q v

_d

A B

+ F

_B

Figure 29.7 A segment of a current-carrying wire located in a magnetic field B. The magnetic force exerted on each charge making up the current is and the net force on the segment of length L is I L ! B.

q v

_d

! B,

Force on a segment of a wire in a uniform magnetic field

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 6

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SAĞ EL KURALI

Hareket yönü Hareket yönü

Manyetik

alan Manyetik

alan Akim veya

yüklü parçaciğin hızı

Akim veya

yüklü parçaciğin hızı

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 7

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AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

8 29.2 Magnetic Force Acting on a Current-Carrying Conductor 911

lustrations, such as in Figure 29.6b to d, we depict a magnetic field directed into the page with blue crosses, which represent the tails of arrows shot perpendicularly and away from you. In this case, we call the field B _in , where the subscript “in” indi- cates “into the page.” If B is perpendicular and directed out of the page, we use a series of blue dots, which represent the tips of arrows coming toward you (see Fig.

P29.56). In this case, we call the field B _out . If B lies in the plane of the page, we use a series of blue field lines with arrowheads, as shown in Figure 29.8.

One can demonstrate the magnetic force acting on a current-carrying conductor by hanging a wire between the poles of a magnet, as shown in Figure 29.6a. For ease in visualization, part of the horseshoe magnet in part (a) is removed to show the end face of the south pole in parts (b), (c), and (d) of Figure 29.6. The magnetic field is directed into the page and covers the region within the shaded cir- cles. When the current in the wire is zero, the wire remains vertical, as shown in Figure 29.6b. However, when a current directed upward flows in the wire, as shown in Figure 29.6c, the wire deflects to the left. If we reverse the current, as shown in Figure 29.6d, the wire deflects to the right.

Let us quantify this discussion by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure 29.7. The magnetic force exerted on a charge q moving with a drift velocity v _d is To find the total force acting on the wire, we multiply the force exerted on one charge by the number of charges in the segment. Because the volume of the segment is AL, the number of charges in the segment is nAL, where n is the number of charges per unit volume. Hence, the total magnetic force on the wire of length L is

We can write this expression in a more convenient form by noting that, from Equa- tion 27.4, the current in the wire is Therefore,

(29.3) F _B ! I L ! B

I ! nqv _d A.

F _B ! (q v _d ! B)nAL q v _d ! q B v _d ! B.

(b) B _in

× ×

I = 0

B _in

× ×

I

B _in

× ×

I

(c) (d)

(a)

Figure 29.6 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field

(blue crosses) is directed into the page. When there is no current in the wire, it remains vertical.

(c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

L

q v _d

A B

+ F _B

Figure 29.7 A segment of a current-carrying wire located in a magnetic field B. The magnetic force exerted on each charge making up the current is and the net force on the segment of length L is I L ! B.

q v _d ! B,

Force on a segment of a wire in a uniform magnetic field

29.2 Magnetic Force Acting on a Current-Carrying Conductor 911

lustrations, such as in Figure 29.6b to d, we depict a magnetic field directed into the page with blue crosses, which represent the tails of arrows shot perpendicularly and away from you. In this case, we call the field B _in , where the subscript “in” indi- cates “into the page.” If B is perpendicular and directed out of the page, we use a series of blue dots, which represent the tips of arrows coming toward you (see Fig.

P29.56). In this case, we call the field B _out . If B lies in the plane of the page, we use a series of blue field lines with arrowheads, as shown in Figure 29.8.

One can demonstrate the magnetic force acting on a current-carrying conductor by hanging a wire between the poles of a magnet, as shown in Figure 29.6a. For ease in visualization, part of the horseshoe magnet in part (a) is removed to show the end face of the south pole in parts (b), (c), and (d) of Figure 29.6. The magnetic field is directed into the page and covers the region within the shaded cir- cles. When the current in the wire is zero, the wire remains vertical, as shown in Figure 29.6b. However, when a current directed upward flows in the wire, as shown in Figure 29.6c, the wire deflects to the left. If we reverse the current, as shown in Figure 29.6d, the wire deflects to the right.

Let us quantify this discussion by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure 29.7. The magnetic force exerted on a charge q moving with a drift velocity v _d is To find the total force acting on the wire, we multiply the force exerted on one charge by the number of charges in the segment. Because the volume of the segment is AL, the number of charges in the segment is nAL, where n is the number of charges per unit volume. Hence, the total magnetic force on the wire of length L is

We can write this expression in a more convenient form by noting that, from Equa- tion 27.4, the current in the wire is Therefore,

(29.3) F _B ! I L ! B

I ! nqv _d A.

F _B ! (q v _d ! B)nAL q v _d ! q B v _d ! B.

(b) B _in

× ×

I = 0

B _in

× ×

I

B _in

× ×

I

(c) (d)

(a)

Figure 29.6 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field

(blue crosses) is directed into the page. When there is no current in the wire, it remains vertical.

(c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

L

q v _d

A B

+

F _B

Figure 29.7 A segment of a current-carrying wire located in a magnetic field B. The magnetic force exerted on each charge making up the current is and the net force on the segment of length L is I L ! B.

q v _d ! B,

Force on a segment of a wire in a uniform magnetic field

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

(9)

AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

9 29.2 Magnetic Force Acting on a Current-Carrying Conductor 911

lustrations, such as in Figure 29.6b to d, we depict a magnetic field directed into the page with blue crosses, which represent the tails of arrows shot perpendicularly and away from you. In this case, we call the field B _in , where the subscript “in” indi- cates “into the page.” If B is perpendicular and directed out of the page, we use a series of blue dots, which represent the tips of arrows coming toward you (see Fig.

P29.56). In this case, we call the field B _out . If B lies in the plane of the page, we use a series of blue field lines with arrowheads, as shown in Figure 29.8.

One can demonstrate the magnetic force acting on a current-carrying conductor by hanging a wire between the poles of a magnet, as shown in Figure 29.6a. For ease in visualization, part of the horseshoe magnet in part (a) is removed to show the end face of the south pole in parts (b), (c), and (d) of Figure 29.6. The magnetic field is directed into the page and covers the region within the shaded cir- cles. When the current in the wire is zero, the wire remains vertical, as shown in Figure 29.6b. However, when a current directed upward flows in the wire, as shown in Figure 29.6c, the wire deflects to the left. If we reverse the current, as shown in Figure 29.6d, the wire deflects to the right.

Let us quantify this discussion by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure 29.7. The magnetic force exerted on a charge q moving with a drift velocity v _d is To find the total force acting on the wire, we multiply the force exerted on one charge by the number of charges in the segment. Because the volume of the segment is AL, the number of charges in the segment is nAL, where n is the number of charges per unit volume. Hence, the total magnetic force on the wire of length L is

We can write this expression in a more convenient form by noting that, from Equa- tion 27.4, the current in the wire is Therefore,

(29.3) F _B ! I L ! B

I ! nqv _d A.

F _B ! (q v _d ! B)nAL q v _d ! q B v _d ! B.

(b) B _in

× ×

I = 0

B _in

× ×

I

B _in

× ×

I

(c) (d)

(a)

Figure 29.6 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field

(blue crosses) is directed into the page. When there is no current in the wire, it remains vertical.

(c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

L q

v _d

A B

+

F _B

Figure 29.7 A segment of a current-carrying wire located in a magnetic field B. The magnetic force exerted on each charge making up the current is and the net force on the segment of length L is I L ! B.

q v _d ! B,

Force on a segment of a wire in a uniform magnetic field

B düzgün manyetik alanında doğrusal tel parçasına etki

eden kuvvet (vektör)

Akım

(sayisal) Telin

uzunluğu

akim yönünde (vektör)

Manyetik

Alan (vektör)

Bu hesaplama arkadaşlara vektörel bir özellik göstermektedir.

Alandaki tel doğrusal

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

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AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

10 912 C H A P T E R 2 9 Magnetic Fields

where L is a vector that points in the direction of the current I and has a magnitude equal to the length L of the segment. Note that this expression applies only to a straight segment of wire in a uniform magnetic field.

Now let us consider an arbitrarily shaped wire segment of uniform cross- section in a magnetic field, as shown in Figure 29.8. It follows from Equation 29.3 that the magnetic force exerted on a small segment of vector length d s in the pres- ence of a field B is

(29.4) where d F _B is directed out of the page for the directions assumed in Figure 29.8.

We can consider Equation 29.4 as an alternative definition of B. That is, we can de- fine the magnetic field B in terms of a measurable force exerted on a current element, where the force is a maximum when B is perpendicular to the element and zero when B is parallel to the element.

To calculate the total force F _B acting on the wire shown in Figure 29.8, we in- tegrate Equation 29.4 over the length of the wire:

(29.5) where a and b represent the end points of the wire. When this integration is car- ried out, the magnitude of the magnetic field and the direction the field makes with the vector d s (in other words, with the orientation of the element) may differ at different points.

Now let us consider two special cases involving Equation 29.5. In both cases, the magnetic field is taken to be constant in magnitude and direction.

Case 1 A curved wire carries a current I and is located in a uniform magnetic field B, as shown in Figure 29.9a. Because the field is uniform, we can take B out- side the integral in Equation 29.5, and we obtain

(29.6)

F _B ! I ! " _a ^b ^d ^s # ^! ^B

F _B ! I " _a ^b ^d ^{s ! B}

d F _B ! I d s ! B

B ds

I

Figure 29.8 A wire segment of arbitrary shape carrying a current I in a magnetic field B experiences a magnetic force. The force on any segment d s is I ds ! B and is directed out of the page. You should use the right-hand rule to confirm this force direction.

(b) d s

B I

I

b

a d s

L′

B

(a)

Figure 29.9 (a) A curved wire carrying a current I in a uniform magnetic field. The total magnetic force acting on the wire is equivalent to the force on a straight wire of length L" running between the ends of the curved wire. (b) A current-carrying loop of arbitrary shape in a uniform magnetic field. The net magnetic force on the loop is zero.

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

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AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 11

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AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

12

912 C H A P T E R 2 9 Magnetic Fields

where L is a vector that points

in the direction of the current I and has a magni-

tude equal

to the length L of the segment. Note that this expression

applies only

to a straight segment of wire in a uniform magnetic field.

Now let us consider an arbitrarily

shaped wire segment

of uniform

cross-

section in a magnetic

field, as shown in Figure 29.8. It follows from Equation 29.3

that the magnetic force exerted on a small segment of vector length

ds in the pres-

ence of a field

B is

(29.4)

where d F ^B is directed

out of the page for the directions assumed in Figure 29.8.

We ca n con sider E quatio n 29.4 as an altern ative d efiniti on of B. Tha t is, we can d e- fine the magnetic field B in terms of a measurable

force exerted on a current

ele-

ment, where the force is a maximum

when B is perpendicular

to the element and

zero when B is parallel to the element.

To cal culate the to tal for ce F ^B acting on the wire shown

in Figure 29.8, we in-

tegrate Equation 29.4 over the length of the wire:

(29.5)

where a and b represent

the end points of the wire. When

this integration

is car-

ried out, the magnitude

of the magnetic field and the direction

the field makes

with the vector ds (in other word s, with the o rienta tion o f the e lemen t) may differ at different points.

Now let us consider

two special

cases involving Equation 29.5. In both cases,

the magnetic field is taken to be constant in magnitude and direction.

Case 1 A curved wire carries

a current I and is located in a uniform

magnetic

field B , as shown in Figure 29.9a. Because the field is uniform,

we can take B out-

side the integral in Equation 29.5, and we obtain

(29.6)

F ^B ! I ! " ^b ^a ^ds ^# ^{! B}

F B ! I " ^b ^a ^{ds !} ^B

dF ^B ! I ds ! B

B ds

I

Figure 29.8

A wire segment of arbitrar y shape carr

ying a current I

in a magnetic field

B experiences a magnetic force. The force on any

segment ds is I d s ! B and is directed out of the page. Y

ou should

use the right-hand rule to confirm this force direction.

(b) d s I B

I

b

a

d s L′

B

(a)

Figure 29.9

(a) A cur ved wire carr

ying a current

I in a uniform magnetic field. The total mag-

netic force acting on the wire is equivalent to the force on a straight wire of length

L" running be-

tween the ends of the cur

ved wire. ( b) A current-carr

ying loop of arbitrar

y shape in a uniform

magnetic field. The net magnetic force on the loop is zero.

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

(13)

AKIM TAŞIYAN BIR ILETKENE ETKIYEN MANYETIK KUVVET

13 912 C H A P T E R 2 9 Magnetic Fields

where L is a vector that points in the direction of the current I and has a magnitude equal to the length L of the segment. Note that this expression applies only to a straight segment of wire in a uniform magnetic field.

Now let us consider an arbitrarily shaped wire segment of uniform cross- section in a magnetic field, as shown in Figure 29.8. It follows from Equation 29.3 that the magnetic force exerted on a small segment of vector length d s in the pres- ence of a field B is

(29.4) where d F

B

is directed out of the page for the directions assumed in Figure 29.8.

We can consider Equation 29.4 as an alternative definition of B. That is, we can de- fine the magnetic field B in terms of a measurable force exerted on a current element, where the force is a maximum when B is perpendicular to the element and zero when B is parallel to the element.

To calculate the total force F

B

acting on the wire shown in Figure 29.8, we in- tegrate Equation 29.4 over the length of the wire:

(29.5) where a and b represent the end points of the wire. When this integration is car- ried out, the magnitude of the magnetic field and the direction the field makes with the vector d s (in other words, with the orientation of the element) may differ at different points.

Now let us consider two special cases involving Equation 29.5. In both cases, the magnetic field is taken to be constant in magnitude and direction.

Case 1 A curved wire carries a current I and is located in a uniform magnetic field B, as shown in Figure 29.9a. Because the field is uniform, we can take B out- side the integral in Equation 29.5, and we obtain

(29.6) F

_B

! I ! "

_a^b

^d ^s # ^! ^B

F

_B

! I "

_a^b

^d ^{s ! B}

d F

_B

! I d s ! B

B ds

I

Figure 29.8

A wire segment of arbitrary shape carrying a current I in a magnetic field B experiences a magnetic force. The force on any segment ds is I ds ! B and is di- rected out of the page. You should use the right-hand rule to confirm this force direction.

(b) d s

B I

I

b

a d s

L′

B

(a)

Figure 29.9

(a) A curved wire carrying a current I in a uniform magnetic field. The total mag- netic force acting on the wire is equivalent to the force on a straight wire of length L" running be- tween the ends of the curved wire. (b) A current-carrying loop of arbitrary shape in a uniform magnetic field. The net magnetic force on the loop is zero.

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

(14)

ÖRNEK-1

14 29.2 Magnetic Force Acting on a Current-Carrying Conductor 911

lustrations, such as in Figure 29.6b to d, we depict a magnetic field directed into the page with blue crosses, which represent the tails of arrows shot perpendicularly and away from you. In this case, we call the field B _in , where the subscript “in” indi- cates “into the page.” If B is perpendicular and directed out of the page, we use a series of blue dots, which represent the tips of arrows coming toward you (see Fig.

P29.56). In this case, we call the field B _out . If B lies in the plane of the page, we use a series of blue field lines with arrowheads, as shown in Figure 29.8.

One can demonstrate the magnetic force acting on a current-carrying conductor by hanging a wire between the poles of a magnet, as shown in Figure 29.6a. For ease in visualization, part of the horseshoe magnet in part (a) is removed to show the end face of the south pole in parts (b), (c), and (d) of Figure 29.6. The magnetic field is directed into the page and covers the region within the shaded cir- cles. When the current in the wire is zero, the wire remains vertical, as shown in Figure 29.6b. However, when a current directed upward flows in the wire, as shown in Figure 29.6c, the wire deflects to the left. If we reverse the current, as shown in Figure 29.6d, the wire deflects to the right.

Let us quantify this discussion by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure 29.7. The magnetic force exerted on a charge q moving with a drift velocity v _d is To find the total force acting on the wire, we multiply the force exerted on one charge by the number of charges in the segment. Because the volume of the segment is AL, the number of charges in the segment is nAL, where n is the number of charges per unit volume. Hence, the total magnetic force on the wire of length L is

We can write this expression in a more convenient form by noting that, from Equa- tion 27.4, the current in the wire is Therefore,

(29.3) F _B ! I L ! B

I ! nqv _d A.

F _B ! (q v _d ! B)nAL q v _d ! q B v _d ! B.

(b) B _in

× ×

I = 0

B _in

× ×

I

B _in

× ×

I

(c) (d)

(a)

Figure 29.6 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field

(blue crosses) is directed into the page. When there is no current in the wire, it remains vertical.

(c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

L q

v _d

A B

+

F _B

Figure 29.7 A segment of a current-carrying wire located in a magnetic field B. The magnetic force exerted on each charge making up the current is and the net force on the segment of length L is I L ! B.

q v _d ! B,

Force on a segment of a wire in a uniform magnetic field

F=(2.4A)(0.750m)ix(1.6T)k= (-2.88j)N

i,j,k birim vektörler -> x, y, z koordinatlari

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II

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KAYNAKLAR

1. http://www.seckin.com.tr/kitap/413951887 (“Üniversiteler için Fizik”, B. Karaoğlu, Seçkin Yayıncılık, 2012).

2.Fen ve Mühendislik için Fizik Cilt-2, R.A.Serway,R.J.Beichner,5.Baskıdan çeviri, (ÇE) K. Çolakoğlu, Palme Yayıncılık.

3. Üniversite Fiziği Cilt-I, H.D. Young ve R.A.Freedman, (Çeviri Editörü: Prof. Dr. Hilmi Ünlü) 12. Baskı, Pearson Education Yayıncılık 2009, Ankara.

4. https://www.youtube.com/user/crashcourse

Dr. Çağın KAMIŞCIOĞLU, Fizik II, Manyetik Alanlar-II 15

Dr. Çağın KAMIŞCIOĞLU

(FZM 114) FİZİK -II