# If a magnetic flux passes through a circular coil when its diameter D, what should be its...

## Question:

If a magnetic flux passes through a circular coil when its diameter D, what should be its diameter (in terms of D) so that only half as much flux passes through it in the same field? Assume that the magnetic field is uniform over the area in both cases.

## Magnetic flux:

The multiplication of the magnetic field and the area where the current is flowing or the magnetic field can be felt known as the magnetic flux. It is the magnetic field lines that change in a short time.

Given data

• The value of the diameter of the circular coil is {eq}D {/eq}
• The value of the magnetic flux is {eq}\dfrac{\phi }{2} {/eq}

The expression for the area of the circular coil is

{eq}{A_s} = \dfrac{\pi }{4}{\left( D \right)^2} {/eq}

The expression for the flux in the current carrying circular coil is

{eq}{\phi _b} = B{A_s}......................(i) {/eq}

Since the flux is half.

The value of the flux is

{eq}{\phi _b} = \dfrac{\phi }{2} = \dfrac{{B{A_s}}}{2}......................(ii) {/eq}

Equate both the equation (i) and (ii).

{eq}B{A_s} = \dfrac{{B{A_N}}}{2} {/eq}

Substitute the value in the above equation.

{eq}\begin{align*} \dfrac{\pi }{4}{D^2} &= \dfrac{{\left( {\dfrac{\pi }{4}{D_N}^2} \right)}}{2}\\ {D_N} &= D\sqrt 2 \end{align*} {/eq}

Thus, the value of the new diameter of the circular coil is {eq}D\sqrt 2 {/eq} 