A rectangular loop with a sliding connector of length l = 1.0 m is situated in a

Question

A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r = 2

Ω

. Two resistances of 6

Ω

and 3

Ω

are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2m/s is

A Rectangular Loop With A Sliding Connector Of Length L = 1....

Options:

A . 6N

B . 4N

C . 2N

D . 1N

Answer: Option C
:
C
Motional emf

e = B v l \Rightarrow e = 2 \times 2 \times 1 = 4

V
This acts as a cell of emf E=4V and internal resistance r=2

Ω

.
This simple circuit can be drwan as follows

Current through the connector

i = \frac{4}{2 + 2} =

1 A

∴

Magnetic force on connector

F_{m} =

=Bil=

2 \times 1 \times 1 = 2

N (Towards left)

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