Question

two coils p and q lie in the same plane and are concentric, coil p has 10T of r=5.0cm and carries a current of 1.0A point q has 20T of r 8.0cm and the current in it is adjusted in the magnitude and direction so that the resultant field at the common center is zero.Draw the diagram to show the relative directions of the two coils and find the magnitude of the coil q

Answer 1

Answer to Question #75180, Physics / Electric Circuits

Two coils $p$ and $q$ lie in the same plane and are concentric, coil $p$ has $10T$ of $r = 5.0cm$ and carries a current of $1.0A$ , coil $q$ has $20T$ of $r = 8.0cm$ and the current in it is adjusted in the magnitude and direction so that the resultant field at the common center is zero. Draw the diagram to show the relative directions of the two coils and find the magnitude of the coil $q$ .

Solution.

If we have just one coil $p$ , magnetic field in its centre:

$$B _ {1} = \frac {\mu_ {0}}{4 \pi} \frac {2 \pi I _ {1} n _ {1}}{r _ {1}} = \frac {1 0 ^ {- 7} \cdot 2 \cdot 3 . 1 4 \cdot 1 \cdot 1 0}{0 . 0 5} = 1. 2 5 6 \cdot 1 0 ^ {- 4} T$$

In our case, magnetic field in the centre of just one coil $q$ :

$$B _ {2} = - B _ {1}$$

So, the current in the coil $q$ :

$$I _ {2} = \frac {4 \pi B _ {2} r _ {2}}{2 \pi n _ {2}} = \frac {1 . 2 5 6 \cdot 1 0 ^ {- 4} \cdot 0 . 0 8}{2 \cdot 3 . 1 4 \cdot 2 0 \cdot 1 0 ^ {- 7}} = 0. 8 A$$

The currents $I_{1}$ and $I_{2}$ in the coils have opposite directions.

The magnetic field in the coil $p$ is directed from us, in the coil $q$ - to us.