The two conductors of a transmission line carry equal current I in opposite directions. The force on each conductor isa)proportional to 7b)proportional to Xc)proportional to distance between the conductorsd)inversely proportional to ICorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

When two parallel conductors carry current in opposite directions, they experience a force of attraction towards each other. This is known as the Ampere's force.

The force on each conductor is given by the formula:

F = μ/2π * I1 * I2 * L/d

where,
F = force per unit length on each conductor
μ = permeability of free space (4π x 10^-7 N/A^2)
I1 and I2 = currents in the two conductors
L = length of the conductors
d = distance between the conductors

Since the two conductors carry equal current in opposite directions, I1 = I2 = I.

Therefore, the force on each conductor can be written as:

F = μ/2π * I^2 * L/d

Proportional to X:

From the above formula, we can see that the force on each conductor is directly proportional to the square of the current (I^2). Therefore, option (d) is incorrect.

The force is also directly proportional to the length of the conductors (L) and the permeability of free space (μ). However, these factors do not depend on the conductors themselves and are constant for a given system. Therefore, options (a) and (c) are also incorrect.

The only factor that depends on the conductors is the distance between them (d). Therefore, the force on each conductor is directly proportional to the inverse of the distance between them. This is option (b).

Hence, the correct answer is option (b) - proportional to X.

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