Name:
Faraday's Law and Lenz's Law
General Overview: Faraday's Law describes how a changing magnetic flux can induce a
current. Magnetic flux is a computation of magnetic field lines penetrating any enclosed area.
If this magnetic flux starts to change with time, an electromotive force (emf) is generated
which will drive an induced current if a conductive material is located along the loop of
interest. Mathematically, Faraday's Law is written as:
Such that the magnitude of emf (in Volts) is equivalent to the change in magnetic flux with
time.
The direction of induced current can be found using Lenz's Law. Lenz's Law states that any
induced current will always flow in a direction that works to minimize the change in magnetic
flux. In other words, any current through a closed loop will create a magnetic field penetrating
the loop area. This magnetic field due to induced current will interact with the external B-field
penetrating the loop in order to decrease the change in flux.
1) A metallic track is located in the midst of a 0.80 T B-field oriented into the page. The right
rod is pulled to the right at a velocity of 0.50 m/s. Solve for the magnitude of emf induced
along the 4 members of this closed area while the rod is moving.
2) A 1.0 m diameter loop of wire rotates at a constant angular velocity along the dotted axis
shown. It rotates in a region where a 0.20 T B-field is directed into the page. At the instant
shown, is an induced current flowing clockwise, counter-clockwise, or is there zero current.
(Input your answer as CW, CCW, or 0)
3) A coil of wire has 5 complete 0.50 m diameter loops. A B-field is directed through the coil
as shown. The B-field strength is ramped down in a linear fashion from 0.50 T to 0.30 T in 1.5
seconds. Solve for the magnitude of emf induced in the coil and think about what direction an
induced current would flow.
Questions 4 and 5 refer to the following situation:
A 1.2 m long wire of semi-conductive material is formed into a right triangle as shown. The
hypotenuse of the triangle is 0.50 m long. The triangle carries a total resistance of 2.0 Ohms.
A magnetic field points into the page and varies with time in the following manner:
B(t) = 0.5 – 0.3t2
4) Solve for the magnitude of induced current through the triangle at t = 1.0 second. Draw
what direction the induced current will flow.
5) Now assume the triangle is made from a completely non-conductive material. Solve for the
magnitude of emf generated around the triangle loop at t = 1.2 seconds.