Question

A steady electric current is flowing through a cylindrical conductor. Then:
A. The electric field at the axis of the conductor is zero
B. The magnetic field at the axis of the conductor is zero.
C. The electric field in the vicinity of the conductor is zero.
D. The magnetic field in the vicinity of the conductor is zero.

Answer 1

Hint: A conductor is a material that conducts electricity easily. It has many free electrons within its body. This property is of great use. Due to this property of the conductor, many devices can be designed. It has many properties, one among which is that whenever a charge is given to a conductor, it resides on the outer surface of the body.

Complete step-by-step answer:
The net electric charge in the body of the conductor is always zero. All the charges flow from the outer surface of the conductor. Whenever potential difference is applied across the conductor, current flows through the surface. But this doesn’t mean that the electric field at the axis of the conductor is zero. If it becomes zero, the current simply can’t flow. Hence option A is incorrect. But for the outside points, the net electric field is always zero which as the net electric field gets canceled out. Hence option C is correct.
The magnetic field intensity can be calculated by Biot-Savertz law. The direction can be obtained by using the right hand thumb rule. As the current passes through the body only, due to symmetry and direction of the magnetic field, using the right hand thumb rule will be zero along the axis. Hence option B. is correct. But the intensity won’t cancel out for the outside points. Hence magnetic field outside the conductor is non zero. Hence option D is also incorrect.

Note: One must be comfortable using Columb’s law and Biot-Savartz law as one can directly get the direction of electric and magnetic fields respectively, without any calculations. The magnetic field’s direction is given by the right-hand thumb rule.