Question

Two concentric current loops lie in the same plane. The outer loop has twice the diameter of the inner loop. The inner loop carries a 1.0 A current in a clockwise direction. What current, and which direction, should the outer loop carry such that the magnetic field in the center of the loops is zero?

Answer 1

Answer: The outer loop should carry a current of 2.0 A.

The current should flow in the counter-clockwise direction

Explanation: Please see the attachments below

Answer 2

Using the relation for the the current in a magnetic loop, the current and direction in the inner loop would be 2.0 amperes in the clockwise direction

Using the relation for the magnetic field in a loop :

• $B =\frac{U_{0}I}{2R}$
• R = Radius ; I = current
• Inner loop Radius = $R_{0} $

• Outer loop Radius = $R_{0} = 2R_{1}$

outer loop = Inner loop

$\frac{I_{0}}{2 \times 2 R_{1}} = \frac{I_{1}}{2R_{1}}$

Current of inner loop = 1.0 ampere

$\frac{I_{0}}{4R_{1}} = \frac{1}{2R_{1}}$

Cross multiply :

$I_{0} \times 2R_{1} = 4R_{1}$

$I_{0} = \frac{4R_{1}}{2R_{1}}$

$I_{0} = 2$

Hence, the current of the inner loop is 2.0 ampere and it is in the clockwise direction.

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