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  • A rectangular loop with a sliding connector of length l =1.0m is situated in a uniform magnetic field B = 2 T, perpendicular to the plane of the loop. Resistance of connector is r2=. Two resistance

A rectangular loop with a sliding connector of length l =1.0m is situated in a uniform magnetic field B = 2 T, perpendicular to the plane of the loop. Resistance of connector is r2=. Two resistances of \mathrm{6\Omega } and \mathrm{3\Omega } are connected as shown in figure. The external force required to keep the connector moving with a constant velocity  \mathrm{\mathrm1\; {v}=2 \mathrm{~ms}^{-1} } is : 

Option: 1

2 N


Option: 2

1 N


Option: 3

4 N


Option: 4

6 N


Answers (1)

best_answer

Motional emf induced in the connection \mathrm{\varepsilon=\mathrm{Blv}=2(1)(2)=4 \mathrm{~V}}

This acts as a cell of emf 4 V and internal resistance \mathrm{2\Omega , 6\Omega } and \mathrm{3\Omega } resistors are in parallel.

\mathrm{\begin{aligned} & \therefore \frac{1}{R_p}=\frac{1}{6}+\frac{1}{3}=\frac{1+2}{6}=\frac{3}{6}=\frac{1}{2} \\ & R_p=2 \Omega \end{aligned} }

? Current through the connector,

\mathrm{=\frac{\varepsilon}{R_p+r}=\frac{4}{2+2}=1 \mathrm{~A} }

Magnetic force on the connector \mathrm{=\mathrm{BI} l=2(1)(1)=2 \mathrm{~N} }

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manish

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