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

Q. A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2 T perpendicular to the plane of loop. Resistance of connector is r = 2Ω . Two resistances of 6Ω and 3Ω are connected as shown in figure. external force required to keep the connector moving with a constant velocity v = 2 ms^-1 is

(a) 6 N

(b) 4 N

(c) 2 N

(d) 1 N

Ans: (c)

Solution : As 6Ω & 3Ω are in parallel .

$ \displaystyle R’ = \frac{6 \times 3}{6+3}$

R’ = 2 Ω

Now R’ is in series with 2 Ω

Equivalent Resistance , R = R’ + 2 = 2 +2

R = 4 Ω

Motional emf in connector is e = Blv

e = 2 × 1 × 2 = 4 V

I = e/R = 4/4 = 1A

The external force required is

F = I l B = 1 × 1 × 2 = 2 N