| A sliding wire of length 0.25 m and having a resistance of \[0.5\Omega \] moves along conducting guiding rails AB and CD with a uniform speed of 4 m/s. A magnetic field of 0.5 T exists normal to the plane of ABCD directed into the page. The guides are short -circuited with resistances of 4 and \[2\Omega \]. as shown. The current through the sliding wire is: |
 |
A) \[0.27\,A\]
B) \[0.37\,A\]
C) \[1.0\,A\]
D) \[0.72\,A\]
Correct Answer: A
Solution :
| the induced emf across the sliding wire \[e=Bv\ell =0.5\times 4\times 0.25=0.5V\] |
| The effective circuit is shown in figure. |
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| The equivalent resistance of the circuit |
| \[r=\frac{4\times 2}{4+2}+0.5=1.83\Omega \] Now, \[i=\frac{V}{R}=\frac{0.5}{1.83}=0.27A\] |
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