A rectangular loop measuring 20 cm x 80 cm is made of heavy copper wire of radiu

Question

A rectangular loop measuring 20 cm x 80 cm is made of heavy copper wire of radius 0.13 cm. Suppose you shove this loop, short side first, at a speed of 0.40 m/s into a magnetic field of 5.0x10-2 T. The rectangle is face on to the magnetic field. What induced current will flow around the loop?

A rectangular loop measuring 20 cm x 80 cm is made of heavy copper wire of radius 0.13 cm. Suppose you shove this loop, short side first, at a speed of 0.40 m/s into a magnetic field of 5.0x10^ - 2 T. The rectangle is face on to the magnetic field. What induced current will flow around the loop?

Explanation / Answer

the area of the loop inside the B will vary form 0 to 0.2*0.8
I assume that 20 cm and 80 cm distance is between the centres of the wire.
A(t)=x(t)*(0.2)=x*0.2
the flux =A(t)*B

emf, =-d/dt=B*0.2*dx/dt=B*v*0.2=4e-3

now lets calculate the resistance of the whole loop:

electrical resistivity = ( electrical resistance * cross-sectional area ) / longitudinal length

a=pi*r^2=3.14*0.0013^2=5.3e-6

L=2*(80+20)=200cm=2m

copper resistivity = 0.0000000168 ohm.m

then R= 0.00632 ohm

the i=/R=0.633 A

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