Exams › JEE Main › Physics

A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The magnitude of the magnetic induction along its axis is:

1. (a) μ0I / 2π2R
2. (b) μ0I / 2πR
3. (c) μ0I / 4πR
4. (d) μ0I / π2R

Correct answer: (d) μ0I / π2R

Solution

The magnetic induction along the axis of a semi-circular wire can be derived using the Biot-Savart law, which shows that the contribution to the magnetic field from each segment of the wire adds up to yield the result of μ0I / π2R. This reflects the unique geometry of the semi-circular shape, which influences the field strength along the axis.

Related JEE Main Physics questions

• A tightly wound solenoid has 2000 turns and a cross-sectional area of 1.5 × 10⁻⁴ m². It carries a current of 2.0 A and is hung at its center with its axis perpendicular to its length so that it can rotate in a horizontal plane. If it is placed in a uniform magnetic field of strength 5 × 10⁻² tesla, and the field makes an angle of 30° with the solenoid axis, what torque acts on the solenoid?
• A cyclotron with dee radius R is used to speed up protons of mass m. An alternating electric field of frequency ν is applied across the dees. For the cyclotron to operate, the magnetic field B and the kinetic energy K of the emerging proton beam are related by:
• A long, straight conductor of radius a carries a constant current I that is spread uniformly over its cross-sectional area. What is the ratio of the magnetic field at a distance a/2 from the axis to the magnetic field at a distance 2a from the axis?
• A charge of 2 μC revolves with a frequency of 6.25 × 10¹² Hz and creates a magnetic field of 6.28 T at a point on the circle. What is the radius of the circular path?
• An electron beam travels through a region where uniform electric and magnetic fields act mutually perpendicular to each other, and both are also perpendicular to the direction of motion of the electrons. If the electric field strength is 20 V m−1 and the magnetic field strength is 0.5 T, the speed of the electrons must be
• A particle having mass m and charge q is first accelerated through a potential difference V and then enters a zone of uniform magnetic field B acting perpendicular to its velocity. If the magnetic field extends over a width d, what is the angle through which the particle’s direction changes on emerging from the field?

⚔️ Practice JEE Main Physics free + battle 1v1 →