Question

A metallic rod of length L is rotated at an angular speed ω normal to a uniform magnetic field B then the heat dissipation after time t , if the resistance of the rod is R, will be

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Answer 1

Given:

A metallic rod of length L is rotated at an angular speed ω normal to a uniform magnetic field B. Resistance of rod is R.

To find:

Heat dissipated after time t.

Calculation:

The EMF induced in the rod due to rotation will be denoted as E ;

$\rm{ \therefore \: E = B \times v \times L}$

$\rm{ = > \: E = B \times ( \omega \times L) \times L}$

$\rm{ = > \: E = B \omega {(L)}^{2} }$

Now, heat generated in time t;

$\rm{ \therefore \: heat = \dfrac{ {(E)}^{2} }{resistance} \times t}$

$\rm{ = > \: heat = \dfrac{ {(B \omega {L}^{2} )}^{2} }{R} \times t}$

$\rm{ = > \: heat = \dfrac{ {B}^{2} { \omega}^{2} {L}^{4} t }{R} }$

So, final answer is:

$\boxed{ \bf{\: heat = \dfrac{ {B}^{2} { \omega}^{2} {L}^{4} t }{R} }}$