Question

For a straight wire carrying steady current in the vertically upward direction as shown below

• A. The magnetic field lines around the wire are directed clockwise and the magnetic field strength at A is more than that at B.
• B. The magnetic field lines around the wire are directed anti-clockwise and the magnetic field strength at A is less than that at B.
• C. The magnetic field lines around the wire are directed clockwise and the magnetic field strength at A and B are the same.
• D. The magnetic field lines around the wire are directed anti-clockwise and the magnetic field strength at A is more than that at B.

Hint:

Remember the right-hand rule for determining the direction of magnetic field lines around a current-carrying conductor. The closer the point is to the conductor, the greater the magnetic field strength.

Answer 1

The Correct Option is D

When a current flows through a wire, it generates a magnetic field around it. The direction of the magnetic field is determined by the right-hand rule, which states:
- If you hold the wire with your right hand such that your thumb points in the direction of the current, your fingers curl in the direction of the magnetic field. Since the current is flowing upward, the magnetic field lines will circulate anti-clockwise when viewed from above.
The strength of the magnetic field is proportional to the distance from the wire. Using Ampere’s Law, we know that the magnetic field strength (\( B \)) around a straight conductor decreases with the increase in distance from the wire: \[ B = \frac{\mu_0 I}{2\pi r} \] Where:
- \( B \) is the magnetic field strength,
- \( \mu_0 \) is the permeability of free space,
- \( I \) is the current,
- \( r \) is the radial distance from the wire.
Thus, the magnetic field strength at point A, which is closer to the wire, will be greater than the magnetic field strength at point B, which is farther from the wire.
Thus, the magnetic field lines are anti-clockwise, and the magnetic field strength at A is more than at B.