Question

The magnetic field due to a circular wire at its center is:
A. in the plane of wire
B. $30^{\circ}$ to the plane of wire
C. perpendicular to the plane of wire
D. none of the above

Answer 1

Hint: Recall the basics of the magnetic field around the circular wire due to an electric current flowing through the circular wire. The direction of the magnetic field at the centre of the circular wire is given by right hand thumb rule. Determine the direction of the magnetic field if the current flowing through the wire is clockwise and anti-clockwise.

Complete answer:
We have given that the magnetic field is at the center of the wire. This magnetic field is due to the current flowing through the circular wire and magnetic field lines at the centre of the circular wire are straight. The direction of the magnetic field is given by right hand thumb rule.

The right hand thumb rule states that if the curled fingers of the right hand gives the direction of the electric current then the direction of the thumb gives the direction of the magnetic field.

Suppose that the direction of the electric current through the circular wire is in the clockwise direction then the direction of the magnetic field is out of the plane of the wire in the upward direction.

If the direction of the electric current through the circular wire is in the anti-clockwise direction then the direction of the magnetic field is in the plane of the wire in the downward direction.

Hence, according to the direction of the electric current, the direction of the magnetic field is in upward or downward direction perpendicular to the plane of the circular wire. Therefore, the direction of the magnetic field at the centre of the circular wire carrying current is perpendicular to the plane of wire.

Hence, the correct option is C.

Note:The students should not forget to consider both the conditions for the direction of electric current through the wire which are clockwise and anti-clockwise. If the direction of current only in an anti-clockwise direction is considered, it will give the direction of magnetic field into the plane of the wire which is not the correct answer.