5. Magnetic forces on current

BvqF

lA

Nn nlAN

dd vlvl

l

A dv

BlIF

InqAvd

BlnqAv

BvnlAq

BvNqF

d

d

dtot

BlIF

Example: A straight wire carrying a current is placed in a region containing a magnetic field. The current flows in the +x direction. There are no magnetic forces acting on the wire. What is the direction of the magnetic field?

sinIlBF sinlBIF Bvd

and between angle -

180or ,0 0sin 0 F1

dv

– drift velocity

N – number of charge carriers in the volume lAn – density of charge carriers (in metals it is density of electrons)

Example: A horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?

B

I

1) left

2) right

3) zero

4) into the page

5) out of the pageB

I

Example: A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?

1) left

2) right

3) zero

4) into the page

5) out of the page

2

Example 1: A rectangular current loop is in a uniform magnetic field. What is the direction of the net force on the loop?

B

x

z

y

1) + x2) + y3) zero4) - x5) - y

Using the right-hand rule, we find that each of the four wire segments will experience a force outwards from the center of the loop. Thus, the forces of the opposing segments cancel, so the net force is zero.

6. Current loop in magnetic field

3

There is no magnetic force on the top and bottom legs, since they are parallel to the B field. However, the magnetic force on the right side is into the page, and the magnetic force on the left side is out of the page. Therefore, the entire loop will tend to rotate.

Example 2: A wire loop is in a uniform magnetic field. Current flows in the wire loop, as shown. What does the loop do?

1) moves to the right2) moves up3) remains motionless4) rotates5) moves out of the page

This is how a motor works !!

Example: If there is a current in the loop in the direction shown, the loop will:

N S

F

F

NS

1) move up

2) move down

3) rotate clockwise

4) rotate counterclockwise

5) both rotate and move

At the North Pole, the magnetic field points to the right and the current points out

of the page. The right-hand rule says that the force must point up. At the south

pole, the same logic leads to a downward force. Thus the loop rotates clockwise.

B field out of NorthB field into South

B

4

mF

I

I

mF

B

Wire and Loop with Electric Current in Magnetic Field

Battery

LoopMagnetic field

Axis of rotation

The loop will rotate (clockwise)

B

N S N S

I

mF

mF

B

N S N S

I

5

6a. Current loop and magnetic moment

'aF

I

IaF

B

b

a '

'

'sin

bb

aa

b

a

FF

FF

IbBF

IaBF

bF

'bF

0 F

Aab

sinsinsin2

2 IABIaBbb

Fa

nNIAM ˆ

sinMB

' B

aF

N – number of loops in the coil

1 NN

aFb

BM

Bn

and in current theofdirection ebetween th angle

and between angle

and ,ˆcoil, thelar toperpendicu ebetween th angle -

b

n̂

n̂

Definition of magnetic

dipole moment:

6

Example 1 : A current-caring circular coil is in uniform magnetic field. The maximum magnitude of the torque on the coil occurs when the angle between the field and magnetic moment is

0 45° 90° 135° 180°

sinB

2

2

Example 2: A coil is oriented initially with its magnetic dipole moment antiparallel to a uniform magnetic field. In this orientation torque is equal to:

A) = 0 B) = max C) 0< < max

7This is unstable equilibrium

Example:

?

?

00.2

00.3

30

10.0

10

M

TB

AI

mr

N

22 94.010.000.310 AmmAM

sinMB

2rA

NIAM

mNTmA 94.030sin00.294.0 2

8