Question

A horizontal overhead powerline is at a height of 4m from the ground and carries a current of 100A from east to west. The magnetic field directly below it on the ground is \( \mu_0 I / 2 \pi r \). What is the magnetic field at this point?

• A. \( 2 \times 10^{-7} \, \text{T} \) southward
• B. \( 5 \times 10^{-7} \, \text{T} \) northward
• C. \( 5 \times 10^{-7} \, \text{T} \) southward
• D. \( 2 \times 10^{-7} \, \text{T} \) northward

Hint:

Use the right-hand rule to determine the direction of the magnetic field due to a current.

Answer 1

The Correct Option is C

Step 1: Formula for magnetic field.
The magnetic field due to a current-carrying conductor is given by: \[ B = \frac{\mu_0 I}{2 \pi r} \] where \( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \), \( I = 100 \, \text{A} \), and \( r = 4 \, \text{m} \).

Step 2: Calculate the magnetic field.
Substitute the given values into the formula: \[ B = \frac{4 \pi \times 10^{-7} \times 100}{2 \pi \times 4} = 5 \times 10^{-7} \, \text{T} \] The direction of the magnetic field is given by the right-hand rule, which points southward.
Thus, the correct answer is (3).