Induced EMF and Inductance

1830s Michael FaradayJoseph Henry

MiBiB ;;M is mutual inductance

Faraday’s Law of Induction

The induced EMF in a closed loop equals the negative of the time rate of change of magnetic flux through the loop

dt

dEMF B

dt

drdE B

A Simple Generator

A circular loop of wire, with resistance R and radius r0 is in a magnetic field which is perpendicular to the plane of the loop. The magnetic field has a constant magnitude B0 and is directed out of the page. If the loop somehow expands so that its radius is given by r=r0+ t2 ( is a constant) what current flows in the loop?

Hw Quiz

The magnetic field between the poles of the electromagnet is uniform, but its magnitude is increasing at the rate of 0.020 T/s. The area of the conducting loop in the field is 120 cm2, and the total circuit resistance, including the meter and the resistor, is 5.0 Ώ. Find the induced EMF and the induced current in the circuit.

S

BSBSSBB 0cos

mVVmsTSdt

dB

dt

BSd

dt

d B 24.0104.2)012.0)(/020.0()( 42

mAAV

R

EMFi 048.0108.4

0.5

104.2 54