Magnetic Induction Review of Chapter 22

Induced EMF (motional EMF) Potential difference (voltage) created by a changing magnetic field that causes current to flow through a wire. e = v B L where e is the electromotive force, v is the relative velocity between the charged object and the field, B is the magnetic field strength and L is the length of the object (or wire) passing through the field. perpendicular The equation above assumes that v, B, and L are mutually

Magnetic Flux Definition: the number of field lines that pass through an area. FB = BA cos Q where FB is the magnetic flux, B is the magnetic field, A is the area of the region that the flux is passing through and Q is the angle between B and A e = DF/Dt this equation for a single conductor is the basis for Faraday’s Law

Faraday’s Law Definition: describes exactly how much EMF is induced by a changing magnetic flux. Equation: e = -N DF Dt

Lenz’s Law Lenz’s law describes the direction of the induced current. Lenz stated that the direction of the induced current always opposes the increase in flux. In other words, the induced current will create a magnetic field opposite to the existing magnetic field causing the current.

Practice Problem A circular loop of wire of negligible resistance and a radius of 20 cm is attached to the circuit shown. Each resistor has a value of 10 W. The magnetic field of the Earth point up as shown and has a value of 5 x 10-5 T. The circular loop rotates about a horizontal axis that passes through the center of the loop at a rate of 500 rev/s and remains connected to the circuit the entire time

Practice Problem (Continued) Determine the magnetic flux through the loop when in the orientation shown in the picture. Determing the maximum magnetic flux through the loop. Estimate the average value of the induced EMF in the loop. Estimate the average current in resistor C

Q1 - Magnetic Flux as shown The flux equals zero because the field points along the loop, never going through the loop.

Q2 - Maximum Flux Flux is at a maximum when the loop is perpendicular to the page. The flux will then be equal to B•A. B = 5 x 10-5 T A = π•r2 = π (.20)2 = .126 F = 6.3 x 10-6 Tm2

Q3 - Average EMF for the Loop e = DF/Dt, and it takes 1/4 turn to go from the minimum to maximum flux. Since it takes 1/500 of a second to make 1 turn, it only takes 1/2000 of a second to reach the first maximum. Using the equation above, the EMF is 6.3 x 10-6 Tm2 /0.0005 s = .013 V

Q4 - Current in Resistor C The circuit can now be treated as if there were a 13 mV battery attached to it. Re of resistors B and C is 5Ω and RT is 15Ω. IT = 8.4 x 10-4 A Since B and C are equal, the current is split equally among them and is 4.2x10-4 A.