Question

Two circular current-carrying loops of wire are shown in the drawing. The inner loop has a radius of R₀ and carries a current I₀, while the outer loop has a radius of 2R₀ and carries a current of 4I₀. The currents are in opposite directions. If R₀ = 0.20 m and I₀ = 1.9 A, determine the magnitude and direction of the net magnetic field at the center of the two loops.

Answer 1

Here as shown in the figure,the 2 concentric circular condctors loops in which the outer conductor has radius carrying a current in clockwise direction as shown.

Also the inner circular conductor loop having a radius carrying a current in the anticlockwise direction. ie, opposite to the direction of outer loop.

We have the magnetic field by the circular conductor loop of radius carrying current given by,

Here the direction of the magnetic field at the centre of circular conductor loop is determined by the Right hand thumb rule in which the thumb indicates direction of field and the fingers directed to the direction of current.

So here the direction of magnetic field of outer loop at centre is inner to the plane of paper,(ie,-z axis).

And the direction of magnetic field of inner loop is outer to the plane of paper perpenducular to plane(ie,+ve z axis),

So.the magnitude of the magnetic field of outer loop at centre,

(ie,acting in the -Z axis,inner to the plane)

Also,the magnitude of the magnetic field of inner loop at centre,

So,the net magnetic field,

So,

So,the Net magnetic field is acting toward -z axis or inner to the plane of paper or coils.

Here given that,

So,magnitude of net magnetic field at the centre C,

Substituting values,

Or,net magnetic field (in vector form) at the centre of loop,(directing inner to the plane)

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