Answers

Force on Electric Current in Magnetic Field

 

Example 1

A straight wire 160 meters long is stretched between 2 towers.

 The wire carries 200 A current and the Earth's magnetic field of 5.0x10-5 T makes an angle of 40 degrees with the wire. What is the magnetic force on the wire?

 

 

The force is given by F = ILBsinq where values for all of the variables are given. Remember that this is a force and the units are N

 

I = 200 A, L = 160 m, B = 5.0x10-5 T, and the angle is 40 degrees

 

 

Example 2

The force on a wire is maximum when it is placed between the pole faces of a magnet. The wire is carrying 9 A, the maximum force is 1.3 N, and the ole faces are 60 cm in diameter. Find the approximate strength of the magnetic field.

 

Once again we use the equation F = ILBsinq

except that it is given that the force is a maximum, therefore the angle is 90 degrees and

F = ILB

 

Solving for B        B = F_max/IL = 1.3 N/(9 A)(0.60 m) = 0.24 T

 

Force on Charge Moving in a Magnetic Field

Example 3

Given that an alpha particles are emitted from a source at a given speed. You are also given the mass, m, of the alpha particle, its speed, v, and charge, q, and that they are bent into a circular path or radius r.

How would you find the magnetic field strength that is required to bend them into a circular path?

We are given that the magnetic force is causing centripetal motion - so must have the form of a centripetal force.

Which is, from before, mv²/r

We also know that the force is perpendicular to the velocity (angle is 90 degrees so sine is 1) at all times for circular motion.

Fmax = qvB = mv²/r

Solving for B    ð   B = mv/qr =

Magnetic Field of Straight Wire, Force Between Two Wires

Example 4

 

Jumper cables - between batteries of 2 cars - are sometimes used to start a stalled vehicle.

Assume that the cable carries a 60 A current and that it can be modelled as a long straight wire. Vacuum permeability, m_o = 8.85x10^-12C²/N·m²

 

a. How strong is the magnetic field 6.0 cm away from the cable?

b. From above, the Earth's magnetic field is 5.0x10-5 T. How do they compare?

 

a.  B_cable =  m_oI/2pd = about 2x10^-4 T

 

b. This is stronger that the Earth's magnetic field

 

Solenoids and Electromagnets

 

Example 5

 

A thin solenoid is 20 cm long and carries a current of 3.0 amps. It has a total of 500 turns of wire.

What is the field inside the solenoid near the center?

 

This is an application of equation 20-8 for the field inside a solenoid.

 

B = m_oIN/L =       T