Along an infinitely long conductor carrying a current of 8 A we keep another conductor of length 5 m carrying a current of 3 A. Both the conductors are 10 cm apart. Find the force on small conductor.a)2.4 X 10-4Nb)9.6 X 10-4Nc)2.6 X 10-6Nd)9.6 X 10-5NCorrect answer is option 'A'. Can you explain this answer?

Question

Along an infinitely long conductor carrying a current of 8 A we keep another conductor of length 5 m carrying a current of 3 A. Both the conductors are 10 cm apart. Find the force on small conductor.&#8203;a)2.4 X 10-4Nb)9.6 X 10-4Nc)2.6 X 10-6Nd)9.6 X 10-5NCorrect answer is option 'A'. Can you explain this answer?

Answer

F=4π×10^-7 i1 i2 l/2π rF= 4π × 10^-7×8×3× 5./2π×10^-2.F= 2×10^-7×8×3× 5 ×100.F=2.4×10^-4.

Answer

I₁=3A
I₂=8A
l=5m
r=0.1m
F=?
Force per unit length on the small conductor is given by:
f= μ_o2I₁I₂/4πr
Total force on the length of small conductor is
F=fl
F= μ_o2I₁I₂ l/4πr
F=4πx10^-7x2x3x8x5/4π x 0.1
F=2.4x10^-4N

Answer

Use F =( u. i1*i2*L)/ 2πr

Answer

To find the force on the small conductor, we can use the concept of the magnetic field produced by a current-carrying conductor.

1. Magnetic Field due to the Infinite Conductor:
The magnetic field produced by an infinitely long conductor can be determined using Ampere's Law. Ampere's Law states that the magnetic field at a point due to an infinitely long straight conductor is directly proportional to the current and inversely proportional to the distance from the conductor.

Let's denote the distance from the infinite conductor as r1. As per the problem, the current in the infinite conductor is 8 A. Therefore, the magnetic field produced by the infinite conductor at the position of the small conductor can be given as:
B1 = (μ₀ * I1) / (2π * r1)

2. Magnetic Field due to the Small Conductor:
Similarly, the magnetic field produced by the small conductor can be determined using the same formula. Let's denote the distance from the small conductor as r2. The current in the small conductor is given as 3 A. Therefore, the magnetic field produced by the small conductor at its position can be given as:
B2 = (μ₀ * I2) / (2π * r2)

3. Force on the Small Conductor:
The force experienced by the small conductor due to the magnetic field produced by the infinite conductor can be given by the formula:
F = I2 * L * B1

Where:
F is the force on the small conductor,
I2 is the current in the small conductor,
L is the length of the small conductor,
B1 is the magnetic field produced by the infinite conductor at the position of the small conductor.

4. Calculating the Force:
Substituting the values of I2 = 3 A, L = 5 m, and B1 = (μ₀ * I1) / (2π * r1), we can calculate the force on the small conductor.

F = 3 A * 5 m * [(μ₀ * I1) / (2π * r1)]

Given that I1 = 8 A, r1 = 10 cm = 0.1 m, and the value of μ₀ (permeability of free space) is a constant, we can substitute these values to calculate the force.

F = 3 A * 5 m * [(μ₀ * 8 A) / (2π * 0.1 m)]

Simplifying the expression, we get:

F = 2.4 * 10^(-4) N

Hence, the correct answer is option 'A' (2.4 * 10^(-4) N).

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