A rectangular loop of wire passes through a region containing a uniform magnetic

Question

A rectangular loop of wire passes through a region containing a uniform magnetic field pointing into the page. The region is 160cm long and 100cm high, and the magnetic field is 0.1 Tesla. A graph of magnetic flux versus time is pictured below.
a) What is the speed of the rectangular wire loop? b) What is the width W of the rectangular wire loop? c) What is the height H of the rectangular wire loop?
A loop wire passes through a region containing a uniform magnetic field pointing into the page. The region is 160cm long and high, and the magnetic field is 0.1 Tesla. A graph of magnetic flu versus time for the rectangular loop is pictured below. (Drawing not to scale) i 100cm 160cm 0 2 4 6 8 10 12 Time(s) a) What is the speed of the rectangular wire loop? b) What is the width W of the rectangular wire loop? c) What is the height H of the rectangular wire loop?

Explanation / Answer

(a) let v= speed of rectangular wire loop

form the graph, the flux is increasing from 2 o 4 seconds, so t= 4-2= 2 seconds

so we can write distance = speed * time

so w= v(2)= 2v ------------(1)

also from t= 4 to t=10 s, the loop is inside and hence the flux is constant and loop covers a distance of 160- w

so 160-w= v (6)=6v ---------------------(2)

adding equations 1 and 2 , we get

160=8v

v= 20 cm/s.

(b) w= 2v

w=2(20)

w= 40 cm.

(c) induced emf= change in flux/ time

e= (60-0)/(4-2)

e= 30 volts

now induced emf e= B H V

30=(0.1)(H)(20)

H= 15 cm.

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