Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by φᵢ. The magnetic flux through the area of the circular coil area is given by φ₀. Which of the following option is correct?

Solution

Physics sir · 4 steps

Every field line that goes up through the coil must come back down through the rest of the plane.

1. Closed field lines. Magnetic field lines have no start or end: they always form closed loops. This is Gauss's law for magnetism, ∮ B⃗ · dA⃗ = 0.
2. Make a closed surface. The infinite plane, closed by a hemisphere at infinity where B falls to zero, encloses a region. So the total flux through the whole plane must be zero.

   φ₀ + φᵢ = 0

3. Follow the lines. Inside the coil, the lines cross the plane in one direction, say upward. Each of them loops around outside the wire and crosses the plane again downward, outside the coil. The outside flux is equal in size and opposite in sign.
4. So. φᵢ = -φ₀, which is option (d).

The idea to keep. The net magnetic flux through any closed surface is zero. If flux goes one way through part of a surface, the same amount comes back through the rest of it.

Answer from the NTA final answer key. Solution by PrepWiser.