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  • A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loop of radius 2r, made

A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loop of radius 2r, made of same material, having the same cross section is connected to the same voltage source, what will be the magnetic field at its centre?

Option: 1

\frac{B}{2}


Option: 2

\frac{B}{4}


Option: 3

2B


Option: 4

B


Answers (1)

The magnetic field at the centre of a circular of conducting loop,

B=\frac{\mu_0 I}{2 r}

[ I = current in the loop and r = radius of the loop ]

If the resistance of the loop in the first case is R then the resistance in the second case,

R^{\prime}=2 R [ Since in the second case the length of the loop is doubled ]

\therefore In the second case, current in the loop I^{\prime}=\frac{1}{2}

\therefore B^{\prime}=\frac{\mu_0 I^{\prime}}{2 \times 2 r}=\frac{\mu_0 \times \frac{1}{2}}{2 r \times 2}=\frac{B}{4}

 

Posted by

Kshitij

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