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  • Solve it, A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circ

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region is

  • Option 1)

    is zero

  • Option 2)

      proportional to r

  • Option 3)

    proportional to 1/ r 

  • Option 4)

    proportional to 1/r2

 

Answers (1)

best_answer

As we discussed in concept

Induced electric field -

\varepsilon = \oint \vec{E }\cdot \vec{dl}= \frac{-d\phi }{dt}

When

A \rightarrow constant

\varepsilon = \oint \vec{E }\cdot \vec{dl}=A\frac{dB}{dt}

B \rightarrow Varying

E= \frac{a^{2}}{2r}\, \frac{dB}{dt}

 

- wherein

E_{inclosed}\, \alpha \frac{1}{r}

a\rightarrow radius

 

 Induced electric field due to cylindrical magnetic field is

                              -\:E\:=\:-\frac{R^{2}}{2r}\:.\:\frac{dB}{dt}

\therefore E\propto \frac{1}{r}


Option 1)

is zero

This option is incorrect.

Option 2)

  proportional to r

This option is incorrect.

Option 3)

proportional to 1/ r 

This option is correct.

Option 4)

proportional to 1/r2

This option is incorrect.

Posted by

Plabita

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