Question:
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 \( \phi \)i. The magnetic flux through the area of the circular coil area is given by \( \phi \)0. Which of the following option is correct?
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 \( \phi \)i. The magnetic flux through the area of the circular coil area is given by \( \phi \)0. Which of the following option is correct?
Show Hint
Magnetic field lines are closed loops (Gauss's law for magnetism), so the net flux through the entire infinite plane is zero: the flux through the coil area must be cancelled by the flux through the rest of the plane.
Updated On: Oct 31, 2026
- \( \phi \)i = \( \phi \)0
- \( \phi \)i < \( \phi \)0
- \( \phi \)i \( > \) \( \phi \)0
- \( \phi \)i = - \( \phi \)0
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The Correct Option is D
Solution and Explanation
Step 1: The field of a current loop forms closed lines. The lines pass through the loop area in one direction (say upward) and return through the plane outside the loop in the opposite direction (downward).
Step 2: Consider the closed surface made by the infinite plane and a hemisphere at infinity (where the field of a dipole vanishes faster than the area grows). By Gauss's law for magnetism the net flux through it is zero.
Step 3: Hence the flux through the whole plane is zero: \(\phi_0+\phi_i=0\), so \(\phi_i=-\phi_0\).
Answer: (D) \(\phi_i=-\phi_0\)
Step 2: Consider the closed surface made by the infinite plane and a hemisphere at infinity (where the field of a dipole vanishes faster than the area grows). By Gauss's law for magnetism the net flux through it is zero.
Step 3: Hence the flux through the whole plane is zero: \(\phi_0+\phi_i=0\), so \(\phi_i=-\phi_0\).
Answer: (D) \(\phi_i=-\phi_0\)
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