Question Detail

MTH 102 PHY 102 Past Questions Objective Question

Question

A magnetic induction of 20µT is applied to long straight current carrying wire of radius 120mm. Find the current in the wire. Take µ0 = 4π x 10^-7 Tm/A.
Options
A 120A
B 1.2A
C 12A
Correct Answer
D 0.12A
Correct Answer

Option C is the correct answer.

Detailed Explanation

The magnetic field (B) at a distance (r) from a long straight current-carrying wire is given by Ampere's law: B = (µ0 * I) / (2πr).Given: B = 20 µT = 20 × 10^-6 T, r = 120 mm = 0.120 m, µ0 = 4π × 10^-7 Tm/A.Rearranging the formula to solve for current I: I = (B * 2πr) / µ0.I = (20 × 10^-6 T * 2π * 0.120 m) / (4π × 10^-7 Tm/A)I = (20 × 0.120 × 2π × 10^-6) / (4π × 10^-7)I = (20 × 0.120) / (2 × 10^-1) (since 2π in numerator and 4π in denominator cancel to 1/2, and 10^-6 / 10^-7 = 10^1)I = (2.4) / (0.2) = 12 A.

Hint

Use Ampere's Law for the magnetic field around a long straight current-carrying wire. Ensure units are consistent.

Question Info