Magnetism & Electromagnetic Induction
Electrodynamics
Current and Fields
Right-Hand Current Rule
To find the direction of the magnetic field due to a current carrying wire, point the thumb of your right hand along the wire in the direction of the current I. Your fingers are now curling around the wire in the direction of the magnetic field.
Example 1
The magnetic field shown in the sketch is due to the horizontal, current carrying wire. Does the current in the wire flow to the left or to the right?
Magnetic Field for a Long, Straight Wire
(1) 
Units: tesla, T
Example 2
Find the magnitude of the magnetic field 1 m from a long, straight wire carrying a current of 1 A.
Magnetic Field at the Center of a Circular Loop
(2) 
Solenoids
Right-Hand-Solenoid Rule: when the fingers of the right-hand curl around a solenoid in the direction of the current, the thumb points in the direction of the magnetic field.
Magnetic Field of a Solenoid
(3) 
Units: tesla, T
Example 3
If you want to increase the strength of the magnetic field inside a solenoid, is it better to (a) double the number of loops, keeping the length the same, or (b) double the length, keeping the number of loops the same?
Magnetic Force
Magnetic Force Right-Hand-Rule
To find the direction
of the magnetic force on a positive charge, start by pointing the fingers
of your right hand in the direction of the velocity, 
.
Now, curl your fingers toward the direction of 
.
Your thumb points in the direction of 
.
If the charge is negative, the force points opposite to the direction
of your thumb.
An alternate method-
To find the direction of the magnetic force on a positive charge, start
by pointing your first finger of your right hand in the direction of
the velocity, .
Then point your second finger in the direction of the magnetic field, .
Your thumb points in the direciton of .
If the charge is negative, the force points opposite to the direciton
of your thumb.
Magnitude of the Magnetic Force, F
(4) 
Example 4
Particle 1, with
a charge 
and
a speed 
,
travels at right angles to a uniform magnetic field. The magnetic force
it experiences is 
.
Particle 2, with a charge 
and
a speed 
,
moves at an angle of 55.0° relative to the same magnetic field. Find (a) the
strength of the magnetic field and (b) the magnitude
of the magnetic force exerted on particle 2.
Mathematical way of writing the magnetic force is using a cross product of vectors:
(5) 
Example 5
A solenoid is 20.0 cm long, has 200 loops, and carries a current of 3.25 A. Find the magnitude of the force exerted on a 15.0 µC charged particle moving at 1050 m/s through the interior of the solenoid, at an angle of 11.5° relative to the solenoid's axis.
Example 6
Three particles travel through a region of space where the magnetic field is out of the paper as shown below in the sketch. For each of the three particles, state whether the particle's charge is positive, negative, or zero.
Example 7
A particle with
a charge of 7.70 µC and a speed of 435 m/s is acted on by both
an electric and a magnetic field. The particle moves along the x axis
in the positive direction, the magnetic field has a strength of 3.20
T and points in the positive y direction, and the electric field points
in the positive z direction with a magnitude of 
.
Find the magnitude and direction of the net force acting on the particle.
Trajectory of a Free Particle
(6) 
Example 8
An electron moving
perpendicular to a magnetic field of 
follows
a circular path of radius 2.80 mm. What is the electron's speed?
Example 9
An electron is accelerated
from rest through a potential difference of magnitude V between infinite
parallel plates 
and 
.
The electron then passes into a region of uniform magnetic field strength
B which exists everywhere to the right of plate .
The magnetic field is directed into the page.
(a) On the diagram above, clearly indicate the direction of the electric field
between the plates.
(b) In terms of V and the electron’s mass and charge, determine the electron's
speed at plate .
(c) Describe in detail the motion of the electron through the magnetic field
and explain why the electron moves this way.
(d) If the magnetic field remains unchanged, what could be done to cause the
electron to follow a straight-line path to the right of plate ?
Forces on Wires
Magnetic Force on a Current Carrying Wire
(7) 
where I is current in the wire, L is the length of the wire, and B is the magnetic field. Units are in Newtons.
Example 10
A copper rod 0.150 m long and with a mass of 0.0500 kg is suspended from two thin, flexible wires, as shown in sketch. At right angles to the rod is a uniform magnetic field of 0.550 T pointing into the page. Find (a) the direction and (b) magnitude of the electric current needed to levitate the copper rod.
Torque Exerted on a Rectangular Loop of Area A
(8) 
Torque Exerted on a General Loop of Area A and N Turns
(9) 
Example 11
A rectangular coil with 200 turns is 5.0 cm high and 4.0 cm wide. When the coil is placed in a magnetic field of 0.35 T its maximum torque is 0.22 Nm. What is the current in the coil?