The area vector of a rectangular loop that is initially Li = 700mm long and w i

Question

The area vector of a rectangular loop that is initially Li = 700mm long and wi = 200 mmwide is aligned with the direction of a uniform magnetic field that has initial magnitudeBi = 500 mT. You want to increase the field magnitude smoothly to Bf = 600mT in 10 s, but you want to have zero induced current in the loop. You plan to accomplish this by changing the loop's length L as you increase the magnetic field.

A- In order to have zero induced current, what must the loop length be after 3.00 s?

B- In order to have zero induced current, what must the loop length be after 10.0 s?

Explanation / Answer

Li = 700 mm = 0.7 m

Wi = 200 mm = 0.2 m

the rate of increase in magnetic filed = (Bf-Bi)/t

= (600 - 500)/10

= 10 mT/s

a)
at t = 3 s, B = Bi + 2*10

= 500 + 3*10

= 540 mT

let L is length of loop at t = 3s.

for zero induced emf

initial magnetic flux = final megntic flux

Ai*Bi = A*B

(Li*Wi)*Bi = L*Wi*B

L = (Li*Bi)/B

= (0.7*500)/530

= 0.6604 m or 660.4 mm <<<<----------Answer

b) at t = 10 s, B = Bi + 10*10

= 500 + 10*10

= 600 mT

let L is length of loop at t = 10s.

for zero induced emf

initial magnetic flux = final megntic flux

Ai*Bi = A*B

(Li*Wi)*Bi = L*Wi*B

L = (Li*Bi)/B

= (0.7*500)/600

= 0.5833 m or 583.3 mm <<<<----------Answer

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