The force experienced by a current carrying conductor of length $L$ and lying parallel to a magnetic field having flux density B is:

Explanation:

Force on a Current-Carrying Conductor in a Magnetic Field

Definition: When a current-carrying conductor is placed within a magnetic field, it experiences a force due to the interaction between the magnetic field and the electric current. This phenomenon is described by the Lorentz force law.

Formula: The force experienced by a current-carrying conductor in a magnetic field is given by the equation:

F = I × L × B × sin(θ)

Where:

• F is the force acting on the conductor.
• I is the current flowing through the conductor.
• L is the length of the conductor within the magnetic field.
• B is the magnetic flux density.
• θ is the angle between the direction of the magnetic field and the direction of the current.

In this context, we are specifically interested in the case where the conductor is parallel to the magnetic field. This means that the angle θ between the direction of the current and the magnetic field is 0 degrees (or 180 degrees if considering the opposite direction).

Correct Option Analysis:

Given that the conductor is parallel to the magnetic field, the angle θ is 0 degrees. The sine of 0 degrees is 0. Therefore, the force experienced by the conductor can be calculated as:

F = I × L × B × sin(0)

Since sin(0) = 0:

F = I × L × B × 0

F = 0

Thus, the force experienced by the current-carrying conductor when it is lying parallel to the magnetic field is 0. This is because the magnetic force is perpendicular to the direction of the magnetic field and the current. When these two are parallel, there is no perpendicular component, and thus no force is exerted.

The correct answer is therefore:

Option 4: 0

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: BIL

This option would be correct if the angle θ were 90 degrees, meaning the conductor is perpendicular to the magnetic field. In that case, sin(θ) would be 1, and the force would be maximized at F = BIL. However, this does not apply when the conductor is parallel to the field.

Option 2: BIL sin(θ)

This is the general formula for the force experienced by the conductor, and it is always correct. However, for the specific case where θ is 0 degrees (parallel), sin(θ) is 0, and thus the force is zero. This option is not incorrect but does not directly provide the specific answer for the given condition.

Option 3: HIL

This option is incorrect because it uses H (magnetic field intensity) instead of B (magnetic flux density). The correct parameter in the context of the Lorentz force law is B, not H.

Conclusion:

Understanding the relationship between a current-carrying conductor and the magnetic field is crucial for determining the resulting force. When the conductor is parallel to the magnetic field, no force is exerted on the conductor as the angle θ is 0 degrees. This leads to the conclusion that the force experienced by the conductor is zero. Thus, the correct option is Option 4.