Electro Magnetic Induction And Alternating Currents Question 465

Question: 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:

Options:

A) 0.27 A

B) 0.37 A

C) 1.0 A

D) 0.72A

Show Answer

Answer:

Correct Answer: A

Solution:

  • The induced emf across the sliding wire

    $ e=Bv\ell =0.5\times 4\times 0.25=0.5,V $

    The effective circuit is .

    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}=0.27,A $



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