A square metal wire loop of side 10 cm and resistance 1 ohm is moved with a constant velocity $(v_{0})$ in a uniform magnetic field of induction $B = 2 w e b e r / m^{2}$ as shown in the figure. The magnetic field lines are perpendicular to the plane to the loop (directed into the paper). The loop is connected to a network of resistors each of value 3 ohms. The resistances of hte lead wire OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milliampere in the loop? Given the direction of current in the loop.

Question

A square metal wire loop of side 10 cm and resistance 1 ohm is moved with a constant velocity

(v_{0})

in a uniform magnetic field of induction

B = 2 w e b e r / m^{2}

as shown in the figure. The magnetic field lines are perpendicular to the plane to the loop (directed into the paper). The loop is connected to a network of resistors each of value 3 ohms. The resistances of hte lead wire OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milliampere in the loop? Given the direction of current in the loop.

Filo · Accepted Answer

Answer: B::C::DSolution: Solution Image

The network behaves like a balanced wheatstone bridge.
The free electrons in the portion MN of the rod have a velocity v in the right direction. Applying Fleming's left hand rule, we find that the force on electron will be towards N. Hence, M will be +ve and N will be negative. Current will flow in clockwise direction.
the induced emf developed is given by

e = v B l = v \times 2 \times 0.1 = 0.2 v

....(i)
Now,

e = I R

e = 10^{- 3} \times 4 \times 4 \times 10^{- 3}

amp....(ii)
from (i) and(ii)

0.2 v = 4 \times 10^{- 3}

∴ v = \frac{4 \times 10 ^{- 3}}{0.2} = 0.02 m / s

.

Question Text	A square metal wire loop of side 10 cm and resistance 1 ohm is moved with a constant velocity $(v_{0})$ in a uniform magnetic field of induction $B = 2 w e b e r / m^{2}$ as shown in the figure. The magnetic field lines are perpendicular to the plane to the loop (directed into the paper). The loop is connected to a network of resistors each of value 3 ohms. The resistances of hte lead wire OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milliampere in the loop? Given the direction of current in the loop.
Answer Type	Text solution:1
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