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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 $ϕ_{i}$ . The magnetic flux through the area of the circular coil is given by $ϕ_{0}$ . Which of the following option is correct?

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$ϕ_{i} > ϕ_{0}$

$ϕ_{i} = - ϕ_{0}$

$ϕ_{i} = ϕ_{0}$

$ϕ_{i} < ϕ_{0}$

answer is A.

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Detailed Solution

Given data: Current=I, Magnetic flux around circular coil $ϕ_{i}$ , $μ_{0}$ is the permeability of free space, a is the radius of the coil, and r is the distance from the center of the coil to the plane.

Concepts used: Magnetic field

Explanation

Magnetic flux due to current carrying around a circular coil is

$ϕ_{i} = - \frac{μ_{0}}{4 π} \frac{2 π a^{2} I}{r^{3}} ϕ_{0} = \frac{μ_{0}}{4 π} \frac{2 π a^{2} I}{r} ϕ_{i} = - ϕ_{0}$

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