Chapter 29: Magnetic Fields
By Tori Cook
This chapter examines the forces that act on moving charges and on current carrying wires in the presence of a magnetic field.
IMPORTANT THINGS TO REMEMBER
KEY EQUATIONS
The magnetic force that acts on a charge q moving with a velocity in a magnetic field is v
If a conductor of length L carries a current I , the force exerted on that conductor when it is placed in a uniform magnetic field B is
Magnetic fields are generated around magnets; electric fields are generated around electric charges
Magnetic fields are measured in Teslas
Magnetic field lines leave south poles and enter north poles
The direction of the force found by the right hand rule is for a positive test charge
If a charged particle moves in a magnetic field so that its initial velocity is perpendicular to the field, the particle moves in a circle with a radius found by the equation
Though electric force acts in the same direction as the electric field, remember that magnetic forces act perpendicular to the magnetic field
Magnetic forces only act on charges when they are in motion, unlike electric fields, which act on stationary charges as well
Because of this, the strength of a magnetic field is proportional to the strength of the charge and its speed
Magnetic forces do no work because the force is perpendicular to the displacement
The angular speed of the particle is
The magnetic force on a curved current-carrying wire is equal to that on a straight wire connecting the end points and carrying the same current
The net magnetic force acting on any closed current loop is zero

QUESTIONS
1. [Easy] An electron travels through a tube along the x axis, with a speed of 8.0e6 m/s.
Surrounding the neck of the tube are coils that create a magnetic field with a magnitude of
0.025T, directed at an angle of 60 degrees to the x axis. Calculate the magnetic force on the electron. v
B
2. [Medium] A wire bent into a semicircle of radius R forms a closed circuit and carries a current
I. A uniform magnetic plane is directed along the positive y axis. Find the magnitude and direction of the magnetic force acting on the straight portion of the wire and on the curved portion.
R
I

3. [Hard] A metal rod having a mass per unit length λ carries a current I . The rod hangs from two vertical wires in a uniform vertical magnetic field. The wires make an angle θ with the vertical when in equilibrium. Determine the magnitude of the electric field.
B
I g
SOLUTIONS
1. To find magnetic force, use the equation
2. The equation for the magnetic force of a current carrying wire is . For this problem, it is easiest to split up the half-circle into two parts. The straight part will be F1 and the curved part will be F2.
For F1, and . This means that can see that this force comes out of the page.
. Using the right hand rule, we

To find the magnitude of F2, we have to remember that the force a curved wire is the same as the force on a straight wire carrying the same current that starts and ends at the same points.
Therefore, the force acting on the curved part will be the same as the force acting on the straight part. However, the current is flowing in the other direction, so the right hand rule tells us that the force is going into the page.
The net force acting on the entire shape is
This solution makes sense because one of the things that I mentioned at the top of the page is that the force acting on any closed loop is zero.
3. For this problem, we will need to define L as the length of each rod and as the tension in each wire. At equilibrium, the forces in both the x and y directions will be equal to 0.