Question

4. A square loop, side L, with resistance R sits in a uniform magnetic field as shown below. The field is directed into the page and the loop initially lies in the plane of the page хх хXX X X х X X х х х х х хх хXX Find the current in the loop under the following conditions a) The loop rotates in/out of the page about any side with constant angular frequency o and the magnetic field, Bo, is static b) The loop rotates in/out of the page with constant angular frequency o and the magnetic field is oscillatory, given by B(t) Bocos(5ot) c) In this case, you don't have to calculate the current - simply sketch the current as a function of time. Specify whether the current is clockwise or counterclockwise The loop is now stationary, lying in the plane of the page as shown. The magnetic field is given by a square wave with period T as shown below: 2T time T

Answer 1

Au X X side L Raistonce- R X X Y X 240ky X X X X ang lan taeg foeg. Als Aauare leopis Rence befahinginfout betcween normal e the andl the magnetic feld chawges veey tiue B. A BA COSO BA COSwt Emf induceal dd clt BA COsut d C Bo A cos cest) df Bo A sinwt lw) E X

CUsreut indered, I R Brt) B cos Swt langing Cas 2A BA Cos O (b COs fot) A Coswt Bo A Cos Swt Coswt Ces A CosB Casf+8) + Cos(Aィe) B A + Cosywt B A 1 Ewt inducad E = d t + E = dt sinbst t 4w ginuwt Bo A 38n6wt + Qinuuwて7

indereol I = R wBgA CBAinbut + nywr I = R BwkBAlnwt +2 inuust R (c) 2T Hexe the clockwise (u88ut