An electricity and magnetism problem by Sudipan Mallick

Electricity and Magnetism Level 3

Four uniform wires $FG$ , $GH$ , $HI$ and $IF$ each of length $l$ and having resistance $R$ , $2R$ , $3R$ and $4R$ respectively are connected together to form a square $FGHI$ . The square is placed in a magnetic field whose induction varies with time according to law $B = Xt$ . Calculate potential difference between $F$ and $G$ .

\frac{3Xl^2}{20}

\frac{3Xl^2}{10}

\frac{Xl^2}{10}

\frac{2Xl^2}{30}

1 solution

A Former Brilliant Member
Mar 11, 2016

Flux through the square loop $\phi = Bl^{2} =Xl^{2}t$
According to Faraday's law, an emf is induce,
$| e | = \dfrac{d\phi}{dt} = Xl^{2}$
Since, this is a closed loop a current flows in it,
$i = \dfrac{e}{R_{total}} = \dfrac{Xl^{2}}{10R}$

Potential difference between F & G $= i \times R_{FG} = \dfrac{Xl^{2}}{10R} \cdot R = \dfrac{ Xl^{2}}{10}$

An electricity and magnetism problem by Sudipan Mallick

1 solution

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