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 :
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.
$$0.72\,A$$
Answer :
$$0.27\,A$$
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 shown in figure.
The equivalent resistance of the circuit
$$\eqalign{ & r = \frac{{4 \times 2}}{{4 + 2}} + 0.5 = 1.83\,\Omega \cr & {\text{Now,}}\,i = \frac{V}{R} = \frac{{0.5}}{{1.83}} = 0.27\,A \cr} $$
The induced emf across the sliding wire
$$e = Bv\ell = 0.5 \times 4 \times 0.25 = 0.5\,V$$
The effective circuit is shown in figure.
The equivalent resistance of the circuit
$$\eqalign{ & r = \frac{{4 \times 2}}{{4 + 2}} + 0.5 = 1.83\,\Omega \cr & {\text{Now,}}\,i = \frac{V}{R} = \frac{{0.5}}{{1.83}} = 0.27\,A \cr} $$
