Magnetic Force - Department of Physics

Magnetic Force

?A

vertical wire carries a current and is in a vertical

magnetic field. What is the direction of the force on the

wire?

? (a)

left

? (b) right

? (c) zero

? (d) into the page

? (e) out of the page

B

I is parallel to B, so

no magnetic force

I

PHY2054: Chapter 19

25

Torque on Current Loop

? Consider

a

rectangular current loop

Forces in left, right branches = 0

? Forces in top/bottom branches cancel

? No net force! (true for any shape)

?

? But

b

there is a net torque!

Bottom side up, top side down (RHR)

? Rotates around horizontal axis

?

¦Ó = Fd = ( iBa ) b = iBab = iBA

?¦Ì

B

b

a

Plane normal is ¡Í B here

= NiA ? ¡°magnetic moment¡± (N turns)

True for any shape!!

? Direction of ¦Ì given by RHR

? Fingers curl around loop and thumb points

in direction of ¦Ì

?

PHY2054: Chapter 19

26

General Treatment of Magnetic Moment, Torque

?¦Ì

= NiA is magnetic moment (with N turns)

? Direction

of ¦Ì given by RHR

¦È

?Torque

depends on angle ¦È between ¦Ì and B

¦Ó = ¦Ì B sin ¦È

PHY2054: Chapter 19

27

Torque Example

?A

3-turn circular loop of radius 3 cm carries 5A current in

a B field of 2.5 T. Loop is tilted 30¡ã to B field.

B

30¡ã

2

2

? ¦Ì = NiA = 3i¦Ð r = 3 ¡Á 5 ¡Á 3.14 ¡Á ( 0.03 ) = 0.0339 A ? m

2

?¦Ó

= ¦Ì B sin 30¡ã = 0.0339 ¡Á 2.5 ¡Á 0.5 = 0.042 N ? m

?Rotation

always in direction to align ¦Ì with B field

PHY2054: Chapter 19

28

Trajectory in a Constant Magnetic Field

?A

charge q enters B field with velocity v perpendicular to

B. What path will q follow?

is always ¡Í velocity and ¡Í B

? Path will be a circle. F is the centripetal force needed to keep the

charge in its circular orbit. Let¡¯s calculate radius R

? Force

x x x x x x x x x x x x x x

B

x x x x x x x x x x x x x x

x x x x x x x x x x x x x x

x x x x x x x x x x x x vx x

F

F

v

v

F

q

R

PHY2054: Chapter 19

29

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