Question

A very long straight conductor is carrying a steady current of \(2.2 \, {A}\). The conductor is placed on a horizontal table such that the current in the conductor is from south to north. If the horizontal component of the earth's magnetic field at the place is \(3.2 \times 10^{-5} \, {T}\), the force per unit length on the conductor is:

• A. \(7.04 \times 10^{-5} \, {T}\)
• B. Zero
• C. \(3.52 \times 10^{-5} \, {T}\)
• D. \(14.08 \times 10^{-5} \, {T}\)

Hint:

When the magnetic field is parallel to the current, the magnetic force on the conductor is zero. This is a key concept in understanding the directional nature of magnetic forces in electromagnetism.

Answer 1

The Correct Option is B

We are given: 
- Current \( I = 2.2 \, {A} \), 
- Magnetic field \( B = 3.2 \times 10^{-5} \, {T} \), 
- The direction of the current is from south to north. 
The force per unit length \( F/L \) on a current-carrying conductor placed in a magnetic field is given by the formula: \[ \frac{F}{L} = B I \sin \theta \] where: - \( B \) is the magnetic field, - \( I \) is the current, - \( \theta \) is the angle between the direction of the current and the magnetic field. Step 1: Analyze the Direction of the Magnetic Field and the Current In this case, the direction of the current is from south to north, and the horizontal component of the magnetic field \( B \) is also in the horizontal plane. The force is calculated based on the angle between the magnetic field and the current direction. 
Since the magnetic field is horizontal and the current is also horizontal, and both are in the same plane, the angle \( \theta \) between the current and the magnetic field is \( 0^\circ \) (as the two vectors are parallel). 
Step 2: Apply the Formula Substituting \( \theta = 0^\circ \) into the equation: \[ \frac{F}{L} = B I \sin 0^\circ = 0 \] 
Thus, the force per unit length on the conductor is zero.
 Conclusion: The force per unit length on the conductor is zero, so the correct answer is Option (2).