Question

What is the net magnetic field at point O?

Answer 1

Hint: First to find the magnetic field at O we need to calculate the magnetic field acting on two wires. Then write the magnetic field due to infinite straight wire second we will write the magnetic field due to circular wire. After writing, add both the magnetic field and from that we will find the net or total magnetic field at point O.

Complete answer:
Here we need to find the net magnetic field at point O and the radius or the circular wire is equal to R.
Now using a magnetic field formula on two different wires where current I is flowing through them.
Case I:
Magnetic field due to the infinite straight wire.
It is represented as,
 $ {B_1} = \dfrac{{{\mu _0}I}}{{2\pi R}} \ldots \ldots \left( 1 \right) $
Where,
I is the current flowing through it.
R is the radius.
Case II:
Magnetic field due to the circular wire.
It is represented as,
 $ {B_2} = \dfrac{{{\mu _0}I}}{{2R}} \ldots \ldots \left( 2 \right) $
Where,
I is the current flowing through it.
R is the radius.
Now to net magnetic field is equal to,
Adding equation (1) and (2) we will get,
 $ {B_{Net}} = {B_1} + {B_2} $
Now putting the respective values we will get,
 $ {B_{Net}} = \dfrac{{{\mu _0}I}}{{2\pi R}} + \dfrac{{{\mu _0}I}}{{2R}} $
Taking out common terms we will get,
 $ {B_{Net}} = \dfrac{{{\mu _0}I}}{{2R}}\left( {1 + \dfrac{1}{\pi }} \right) $ .

Note:
Remember that here the word magnetic field describes the magnetic influence on moving electric charges, electric currents and magnetic materials. Note that when a charge moves in a magnetic field expresses a force that is perpendicular to its own velocity and the magnetic field. Keep in mind that to determine the direction of magnetic force we will have to use the right hand thumb rule.