Question

Current flows through uniform, square frames as shown in the figure. In which case is the magnetic field at the centre of the frame not zero?

• A. A
• B. D
• C. C
• D. B

Hint:

When dealing with magnetic fields due to current, use the principle of superposition. The magnetic fields due to currents along different sides of a square may add up or cancel out depending on the direction of the currents.

Answer 1

The Correct Option is C

In this problem, we are asked to determine which configuration of current in square frames produces a non-zero magnetic field at the centre of the frame. 
Case A: Current in opposite directions along opposite sides of the square In this case, the currents flowing along opposite sides of the square will produce magnetic fields that cancel each other out at the centre of the square. Therefore, the magnetic field at the centre is zero. 
Case B: Current in the same direction along opposite sides In this case, the currents flowing in the same direction along opposite sides of the square will produce magnetic fields at the centre that also cancel out due to symmetry. Hence, the magnetic field at the centre remains zero. 
Case C: Current in the same direction along all sides of the square In this configuration, all the currents flow in the same direction along the sides of the square. This produces a net magnetic field at the centre of the square, as the individual contributions from each side add up rather than cancel. Therefore, the magnetic field at the centre is non-zero. 
Case D: Current in opposite directions along adjacent sides In this case, the currents along adjacent sides of the square will create opposing magnetic fields, resulting in a cancellation at the centre of the square. 
Hence, the magnetic field at the centre is zero. Therefore, the correct answer is option (C) because the magnetic field at the centre of the frame is non-zero when the current flows in the same direction along all sides of the square.