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  • Confused! kindly explain, - Electromagnetic Induction - BITSAT

When a ‘J’ shaped conducting rod is rotating in its own plane with constant angular velocity ω about one of its ends P, in a uniform magnetic field \vec{B} (directed normally into the plane of paper) then magnitude of emf induced across it will be

 

  • Option 1)

    Bw\sqrt{L^{2}+l^{2}}

  • Option 2)

    \frac{1}{2}BwL^{2}

  • Option 3)

    \frac{1}{2}Bw\left ( L^{2}+l^{2} \right )

  • Option 4)

    \frac{1}{2}Bwl^{2}

 

Answers (1)

best_answer

As learnt in

Motional E.m.f due to rotational motion -

Conducting rod \rightarrow

\varepsilon =\frac{1}{2}Bl^{2}\omega =Bl^{2}\pi\nu

 \nu \rightarrow f\! r\! equency

T \rightarrow Time\; period

 

- wherein

 

 This system can be replaced by a single rod of length = \sqrt{l^{2}+L^{2}}

\therefore  E.m.f induced = \frac{1}{2}B\omega \left ( l^{2}+L^{2} \right )


Option 1)

Bw\sqrt{L^{2}+l^{2}}

This option is incorrect

Option 2)

\frac{1}{2}BwL^{2}

This option is incorrect

Option 3)

\frac{1}{2}Bw\left ( L^{2}+l^{2} \right )

This option is correct

Option 4)

\frac{1}{2}Bwl^{2}

This option is incorrect

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