Moving Charges and Magnetism Problems - Numerical 06

Two concentric circles of radius 2 cm and 4 cm respectively carry currents of 2A and 4A in a clockwise direction. What is the net magnetic field at the center? If the direction of current in the inner circle is reversed, what is net magnetic field at the center?

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Suggested solution:

Suggested solution:

The figure below shows concentric circular coils and current flowing in them.

B₁ = magnetic field at O due to coil of radius (r₁) = 2cm

B₂ = magnetic field at O due to coil of radius (r₁) = 4cm

B₂ = magnetic field at O due to coil of radius (r₂) = 4cm

Since both

are in the same direction, the resultant field. B is also the same.

If the direction of the current in the inner circle is reversed, the direction of B₁ reverses. Now B₁ and B₂ are equal in magnitude and opposite in direction. Hence the-net magnetic field is zero.