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 Φi;. The magnetic flux through the area
of the circular coil area is given by Φo
Which of the following option is torrect?
Options 1.Φi= Φo
2. Φi<Φo
3.Φi> Φo
4.Φi= -Φo​

Answer 1

Given that,

Current = I

Inside magnetic flux $\phi=\phi_{i}$

Outside magnetic flux $\phi=\phi_{o}$

We know that,

The magnetic field lines form a closed loop, therefore all outgoing from circular hole passing through the infinite plane. Because the magnetic field lines going inside is equal to the magnetic field lines coming out.

$B_{i}=B_{o}$

The magnetic flux inside is  

$\phi_{i}=B_{i}\cdot A$

The magnetic flux outside is

$\phi_{o}=B_{o}\cdot A$

So, The magnetic flux inside the coil is equal and opposite to the outside magnetic flux of the coil.

$\phi_{i}=-\phi_{0}$

Hence, (4) is correct option.