Question

Two similar circular loops of radius R, are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and $I\sqrt 3$ respectively. The magnetic field at the centre of the coil is
(A) $\dfrac{{{\mu _0}I}}{{2R}}$
(B) $\dfrac{{{\mu _0}I}}{R}$
(C) $\dfrac{{4{\mu _0}I}}{R}$
(D) $\dfrac{{\sqrt 3 {\mu _0}I}}{R}$

Answer 1

Hint : To solve the question we have to know about the magnetic field. We know that, Magnetic Field is the region around a magnetic material or a moving electric charge within which the force of magnetism acts. Typically, a magnetic field can be illustrated in two different ways. The magnetic field can be mathematically described as a vector field.

Complete Step By Step Answer:
The magnetic field at the center of the circular coil of radius R carrying current I is given by,
$B = \dfrac{{{\mu _0}I}}{{2R}}$ …………… $(1)$
The magnetic field at the centre of the circular coil of radius R carrying $\sqrt 3 I$ is given by,
$B' = \dfrac{{\sqrt 3 {\mu _0}I}}{{2R}} = B\sqrt 3$ (From equation $1$ )
The net magnetic field,
${B_n} = \sqrt {{B^2} + 3{B^2}} = 2B$
${B_n} = 2.\dfrac{{{\mu _0}I}}{{2R}} = \dfrac{{{\mu _0}I}}{R}$
Then the correct option will be B.

Note :
We have to keep in our mind that, At all times the direction of the magnetic field is shown by the direction of the magnetic flux lines. The strength of a magnet has to do with the spaces between the magnetic flux lines. The closer the flux lines are to each other, the stronger the magnet is. We also have to know about the unit of magnetic field. We know that, The Magnetic Field is the space around a magnet or current carrying conductor around which magnetic effects can be experienced. Furthermore, it is a vector quantity and its SI unit is Tesla (T).