Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What potential difference ratio should be applied across them so that the magnetic field at their centres is the same?

Question

Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What potential difference ratio should be applied across them so that the magnetic field at their centres is the same? (A) 2 (B) 3 (C) 4 (D) 6

Tardigrade Admin · Accepted Answer

The magnetic field at the centre of a circular coil,

B_{centre} = \frac{μ _{0} N i}{2 r}

∵ i = \frac{V}{R}

,
and

R = \frac{V A}{ρ \cdot 2 π r}

∴ B_{centre} = \frac{μ _{0} N V A}{4 ρ \cdot π r ^{2}}

Where,

A =

area of cross-section of the wire
According to the question,

B_{1} = B_{2} = \frac{V _{1}}{r _{1}^{2}} = \frac{V _{2}}{r _{2}^{2}}

\Rightarrow \frac{V _{1}}{( 2 r _{2} ) ^{2}} = \frac{V _{2}}{r _{2}^{2}}

\Rightarrow V_{1} = 4 V_{2}

Ratio of potential difference

\frac{V _{1}}{V _{2}} = 4

Q. Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What potential difference ratio should be applied across them so that the magnetic field at their centres is the same?

2

3

4

6

Q. Two circular coils $1$ and $2$ are made from the same wire but the radius of the first coil is twice that of the second coil. What potential difference ratio should be applied across them so that the magnetic field at their centres is the same?