Chapter 19 Magnetic Force on Charges and Current- Carrying Wires

This force acts in the direction perpendicular to the plane defined by the vectors v and B as indicated by the right-hand rule! WARNING: cross-product (NOT simple multiplication!) DON’T FORGET: Forces have directions!

Thumb points in the direction of the current. Fingers point in the direction of the magnetic field. Palm faces the direction of the magnetic force.

TeslaWeber/m 2

1 Tesla is a very strong magnetic field. So, magnetic fields are often measured in the cgs (i.e., centimeter, gram, second) unit of Gauss. 1 Tesla = 10 4 Gauss The Earth’s magnetic field is about 0.5 Gauss near the surface.

A proton moves at right angles to a magnetic field of 0.1 T with a speed of 2.0 X 10 7 m/s. Find the magnitude of the acceleration.

Remember when we talked about the motion of charges in a wire…. E A Vd tVd t The charges move with an average velocity v d.

The magnetic force on a wire with N charge carriers moving with velocity v d in a uniform magnetic field B should just be the vector sum of the force on each individual charge. Since the average velocity is the same for all N charge carriers, the magnetic force acts in the same direction (on average) on all the charge carriers. Therefore... Where  is the angle between the long dimension of the wire and the magnetic field. The force acts in the direction perpendicular to both.

N = Number of charge carriers n = number of charge carries per unit volume A = cross-sectional area of wire L = length of wire

But recall our definition of current in a wire... Substituting, we get the simpler expression:

So, the maximum value of the magnetic force on a current carrying wire occurs when the wire is perpendicular to the magnetic field and has the value... Hey, Mr. Sluggo. Magnetic Force on a wire is named after me!

So what happens if we put a loop of wire carrying current I in a magnetic field? B I The currents in the top and bottom of this loop are anti-parallel and parallel to the magnetic field. Therefore, sin  = 0. So the magnetic forces on the top and bottom of the loop are 0!

B I On the left side of the loop, we use the right- hand rule to determine that the force is out (toward us). On the right side of the loop, we use the right- hand rule to determine that the force is in (away from us).

In each case,  = 90 o, sin  = 1, so So, the magnitude of the force on the left side of the loop is the same as the magnitude on the right side of the loop. What, therefore, is going to happen to the loop in this magnetic field?

B I The loop rotates! The magnetic force produces a TORQUE on the current loop, causing it to rotate. In this case, the loop rotates counterclockwise as viewed from above... a/2 b

B I The loop rotates! The magnetic force produces a TORQUE on the current loop, causing it to rotate. In this case, the loop rotates counterclockwise as viewed from above... a/2 b

B I The loop rotates! The magnetic force produces a TORQUE on the current loop, causing it to rotate. In this case, the loop rotates counterclockwise as viewed from above... a/2 b

Where  is the angle between the normal to the loop and the magnetic field. Top View: B I normal  x The normal is the direction perpendicular to the plane of the loop of wire.

If the loop has N turns, then the torque becomes... A small circular coil of 20 turns of wire lies in a uniform magnetic of 0.5 T so that the normal to the plane of the coil makes an angle of 60 o with the direction of B. The radius of the coil is 4 cm, and it carries a current of 3 A. What is the magnitude of the torque on the coil?

x x x x x side view N = 20 turns B = 0.5 T I = 3 A A =  (.04) 2  = 60 o 60 o top view

x x x x x side view I 60 o top view I x If the current flows clockwise around the loop (viewed face on), which way does the loop rotate? The force on the left side of the loop is toward the top of the top view diagram.

CLOCKWISE! The force on the right side of the loop is toward the bottom of the top view diagram. These two forces combine, both creating a torque in the same direction, causing the loop to rotate x x x x x side view I 60 o top view I x