-Lenz’s Law-Induced

Current and Electric Fields

AP Physics C

Mrs. Coyle

Faraday’s Law of Induction

• The emf, E induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit”

• Note: The induced emf and the change in flux have opposite algebraic signs

Bdε

dt

What is the direction of the induced current?

• Lenz’s Law: The induced current has a magnetic field that opposes the original change in flux through the area enclosed by the loop.

• Indicated by minus (–) sign in Faraday’s equation.

• Heinrich Lenz

In which direction is the current induced in the loop?

Answer: Clockwise, because as the bar moves to the right, more field lines are in the loop. The current should act in the (opposite) direction to weaken the magnetic flux (field).

Example: Change in Area

• The new smaller area contains less field lines (in the area), so the current will act in direction to strengthen the magnetic field, so the current will be induced clockwise.

What is the direction of the induced current?

Before After

Problem 30.In Figure P31.30, the bar magnet is moved toward the loop. Is Va – Vb positive, negative, or zero? Explain.

Figure P31.30

http://www.walter-fendt.de/ph14e/generator_e.htm

Generator

Induced emf and Electric Fields

• An electric field is created in the conductor as a result of the changing magnetic flux

• Even in the absence of a conducting loop, a changing magnetic field will generate an electric field in empty space

• This induced electric field is nonconservative– Unlike the electric field produced by stationary

charges

Induced emf and Electric Fields

• For any closed path

• Faraday’s Law

• Faraday’s law general form (one of Maxwell’s four equations):

Bdd

dtE s

emf dE s

Bd

emfdt

Note

• The induced electric field that is generated by a changing magnetic field is a nonconservative field

• The field cannot be an electrostatic field because if the field were electrostatic, and hence conservative, the line integral of E.ds would be zero and it isn’t

Problem 32 For the situation shown, the magnetic field changes with time according to the expression B = (2.00t3 – 4.00t2 + 0.800)T, and r2 = 2R = 5.00 cm. (a)Calculate the magnitude and direction of the force exerted on an electron located at point P2 when t = 2.00 s.(a)At what time is this force equal to zero?

Hint: F = qE + qv x BFE =qE(Why is FB = 0?)