Question

A sliding wire of length $0.25\text{m}$ and having a resistance of $0.5\Omega$ moves along conducting guiding rails $\text{AB}$ and $\text{CD}$ with a uniform speed of $4{\text{ms}}^{-1}$. A magnetic field of $0.5\text{T}$ exists normal to the plane of $\text{ABCD}$ directed into the page. The guiding rails are short-circuited with resistances of $4\Omega$ and $2\Omega$ as shown. The current through the sliding wire is

• A. $0.72\text{A}$
• B. $0.37\text{A}$
• C. $0.27\text{A}$
• D. $1.0\text{A}$

Answer 1

The correct option is C $0.27\text{A}$


When a conductor moves in a magnetic field, then motional emf induced is given by , $e=Blv$

(Where $B,l$ and $v$ are mutually perpendicular to each other)

Induced EMF, $e=0.5\times 0.25\times 4=0.5\text{V}$

Induced current, $i=\frac{e}{R^{\prime }}=\frac{e}{\frac{R_1{R}_2}{R_1+R_2}+r}$

Substituting the data given in the question,

$i=\frac{0.5}{\frac{4\times 2}{4+2}+0.5}=\frac{0.5\times 6}{8+3}=\frac{3}{11}=0.27\text{A}$

Hence, option (c) is the correct answer.