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A conducting bar pulled with a constant speed v on a smooth conducting rail. The region has a steady magnetic field of induction B as shown in the figure. If the speed of the bar is doubled then the rate of heat dissipation will

Option: 1

remain constant


Option: 2

become quarter of the initial value


Option: 3

become four fold


Option: 4

get doubled.


Answers (1)

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\mathrm{\text { The induced emf between } \mathrm{A} \text { and } \mathrm{B}=\mathrm{E}=\mathrm{B} \ell \mathrm{v}}

\mathrm{\Rightarrow \quad \text { The induced current }=\mathrm{i}=\frac{\mathrm{E}}{\mathrm{R}}}

\mathrm{\Rightarrow \quad \mathrm{i}=\frac{\mathrm{B} \ell \mathrm{v}}{\mathrm{R}}}

\mathrm{\text { The electrical power }=\mathrm{P}=\mathrm{i}^2 \mathrm{R}}

\mathrm{=\frac{\mathrm{B}^2 \ell^2 \mathrm{v}^2}{\mathrm{R}}}

Since v is doubled, the electrical power, becomes four times. Since heat dissipation per second is proportional to electrical power, it becomes four fold.

 

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avinash.dongre

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