Magnetic Flux Change In each case below a rectangular loop o

Magnetic Flux Change In each case below, a rectangular loop of wire is moving to the right at 4 m/s into a region with a uniform magnetic Held pointing into the page. In Case B, the field is four times as strong as in Case A. The rectangular loops have different widths and heights, but they are made from identical wires. At the instant shown, they are hallway into the magnetic field regions. Is the rate of change in magnetic flux in the loop in Case A greater than, less than, or equal to the rate of change in magnetic flux in the loop in Case B at the instant shown?

Solution

Area of the loop inside the magnetic field:

For case A

Aa = 0.08*L <--- L = length of the loop inside the magnetic field

similarly for case B

Ab = 0.02*L

For case A:

Ba = Bo

and for case B:

Bb = 4*Bo

So, flux through the loop :

For case A:

Qa = Ba*Aa = Bo*0.08*L

for case B

Qb = Bb*Ab = 4Bo*0.02*L

So, rate of change of flux:

for case A :

dQa/dt = Bo*0.08*dL/dt

= Bo*0.08*v

= Bo*0.08*4

= 0.32*Bo

for case B

dQb/dt = 4Bo*0.02*dL/dt

= 4*Bo*0.02*v

= 0.08*4*Bo

= 0.32*Bo

So, for both the cases, the rate of change of flux is same <----------answer