Consider the following statements: The force per unit length between two stationary parallel wires carrying (steady) currents____.A. is inversely proportional to the separation of wires.B. is proportional to the magnitude of each current.C. satisfies Newton's third law. Out of these_____.a)A and B are correctb)B and C are correctc)A and C are correctd)A, B and C are correctCorrect answer is option 'D'. Can you explain this answer?

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Answer

Explanation:

The force per unit length between two stationary parallel wires carrying steady currents depends on the separation of wires, the magnitude of each current, and satisfies Newton's third law. Let's discuss each statement in detail:

A. The force per unit length between two stationary parallel wires carrying steady currents is inversely proportional to the separation of wires.
- This statement is correct. According to Ampere's law, the magnetic field produced by a current-carrying wire decreases with distance from the wire. Therefore, as the separation between the wires increases, the magnetic field produced by one wire at the position of the other wire decreases, leading to a decrease in the force per unit length between the wires.

B. The force per unit length between two stationary parallel wires carrying steady currents is proportional to the magnitude of each current.
- This statement is correct. The force between two parallel wires carrying currents is given by the equation F = (μ₀I₁I₂L)/(2πd), where F is the force per unit length, I₁ and I₂ are the magnitudes of the currents in the wires, L is the length of the wires, d is the separation between the wires, and μ₀ is the permeability of free space. As the magnitude of each current increases, the force per unit length between the wires also increases.

C. The force per unit length between two stationary parallel wires carrying steady currents satisfies Newton's third law.
- This statement is correct. Newton's third law states that for every action, there is an equal and opposite reaction. In the case of two parallel wires carrying currents, the force per unit length on one wire due to the other wire is equal in magnitude and opposite in direction to the force per unit length on the other wire due to the first wire. This satisfies Newton's third law.

Therefore, all three statements (A, B, and C) are correct.

In summary, the force per unit length between two stationary parallel wires carrying steady currents is inversely proportional to the separation of wires, proportional to the magnitude of each current, and satisfies Newton's third law.

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