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  • A battery is connected between two points A and B in the circumference of a uniform conducting ring. AB of the ring subtends an angle <img alt="\theta" src="https://entrancecorner.oncodecogs.c

A battery is connected between two points A and B in the circumference of a uniform conducting ring. AB of the ring subtends an angle \theta at the centre. The value of the magnetic induction at the centre due to the current in the ring is:

 

Option: 1

Zero, only if \theta = 180\degree


Option: 2

Zero, for all values of \theta


Option: 3

Proportional to 2(180 - \theta)


Option: 4

Inversely proportional to r


Answers (1)

best_answer

The field due to the arc at the centres is given by:

                B = \frac{\mu_{0}i}{4\pi r} \phi

\therefore B _{net}= \frac{\mu_{0}i_{1} \theta}{4\pi r} (\cdot) + \frac{\mu_{0}i _{2}(2\pi - \theta)}{4\pi r} (\times)

B _{net}= V_{A} - V_{B} = i1R1 = i2R2

\implies i2 = i1\frac{R1}{R2}

            i2 = i1\frac{L1}{L2}                [\therefore L = r\theta] (arc length)

            i2 = \frac{i1 \theta }{2\pi - \theta}

\therefore B _{net}= \frac{\mu_{0}i_{1} \theta}{4\pi r} (\cdot) + \frac{\mu_{0}i _{1}\theta}{4\pi } (\times) = 0

 

i.e., the field at the centre of the coil is zero and is independent of \theta.

Posted by

rishi.raj

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