Question

A long straight wire carrying a current 3 A produces a magnetic field \( B \) at a certain distance. The current that flows through the same wire will produce a magnetic field \( \frac{B}{3} \) at the same distance is:

• A. 1.5 A
• B. 1 A
• C. 2.5 A
• D. 3 A
• E. 5 A

Hint:

When the magnetic field is inversely proportional to the current, reducing the magnetic field by a factor of 3 requires reducing the current by the same factor.

Answer 1

The Correct Option is B

The magnetic field produced by a current \( I \) in a long straight wire is given by the formula: \[ B = \frac{\mu_0 I}{2 \pi r} \] where: - \( B \) is the magnetic field at distance \( r \),
- \( I \) is the current,
- \( \mu_0 \) is the permeability of free space,
- \( r \) is the distance from the wire.
Given that a current of 3 A produces a magnetic field \( B \), if we decrease the magnetic field by a factor of 3, i.e., we want the new magnetic field to be \( \frac{B}{3} \), we can apply the same formula to solve for the new current \( I' \).
Let the new current be \( I' \), then: \[ \frac{B}{3} = \frac{\mu_0 I'}{2 \pi r} \] Since the original magnetic field is given by \( B = \frac{\mu_0 3}{2 \pi r} \), we can equate the two expressions: \[ \frac{\mu_0 3}{2 \pi r} \times \frac{1}{3} = \frac{\mu_0 I'}{2 \pi r} \] Simplifying, we get: \[ I' = 1 { A} \] Thus, the current required to produce a magnetic field \( \frac{B}{3} \) at the same distance is 1 A.
Thus, the correct answer is option (B) 1 A.