Question

A 1 cm straight segment of a conductor carrying 1 A current in \( x \)-direction lies symmetrically at the origin of Cartesian coordinate system. The magnetic field due to this segment at point (1m, 1m, 0) is:

• A. \( 1.0 \times 10^{-9} \, \text{T} \)
• B. \( -1.0 \times 10^{-9} \, \text{T} \)
• C. \( \frac{5.0}{\sqrt{2}} \times 10^{-10} \, \text{T} \)
• D. \( -\frac{5.0}{\sqrt{2}} \times 10^{-10} \, \text{T} \)

Hint:

The Biot-Savart law provides a way to calculate the magnetic field produced by a current-carrying element.

Answer 1

The Correct Option is C

Step 1: The setup. The magnetic field due to a current-carrying segment is given by the Biot-Savart law. The formula for the magnetic field at a point due to a current is: \[ B = \frac{\mu_0 I}{4\pi} \cdot \frac{dl \times r}{r^3} \]

Step 2: Applying the formula. For the given setup, the magnetic field at point (1m, 1m, 0) is calculated to be \( 5.0 \times 10^{-10} \, \text{T} \), corresponding to option .