Question

A circular coil A of radius ‘r’ carries current ‘i’. Another circular coil B of radius ‘2r’ carries current ‘i’. The magnetic fields at the centres of the circular coils A and B respectively are in the ratio of K : 1. Find K?

Answer 1

Answer:

2

Step-by-step explanation:

Given :

A circular coil 'A' of :

• Radius = r
• Current = i

A circular coil 'B' of :

• Radius = 2r
• current = i

Ratio of their magnetic fields at centres = K : 1

To find :

The value of K

Solution :

We know that, if B is the magnetic field of the circular coil at the centre. R be the radius and I be the current passing through it, then,

$\boxed{\mathrm{B = \dfrac{\mu_{\circ}I}{2R}}}$

So, writing in the proportional manner, we get,

$\boxed{\mathrm{B \propto \dfrac{I}{R}}}$

So, Let Magnetic field for A and B is $B_A$ and $B_B$

Thus,

$\implies \mathrm{\dfrac{B_A}{B_B} = \dfrac{I_A}{I_B}.\dfrac{R_B}{R_A}}$

$\implies \mathrm{\dfrac{B_A}{B_B} = \dfrac{i}{i} .\dfrac{2r}{r} }$

$\implies \mathrm{\dfrac{B_A}{B_B} = \dfrac{\not{i}}{\not{i}} .\dfrac{2\not{r}}{\not{r}} }$

$\implies \mathrm{\dfrac{B_A}{B_B} = \dfrac{2}{1} }$

$\therefore \underline{\boxed{\mathbf{B_A : B_B = 2 : 1}}}$

Thus, K : 1 = 2 : 1

$\boxed {\bf{K = 2}}$

Hope it helps!!