Two straight wires A and B of lengths 10 m and 12 m carrying currents of 4.0 A and 6.0 A respectively in opposite directions lie parallel to each other at a distance of 0.03 m. Estimate the force on a 15 cm section of the wire B near its centre.

Solution

Given,
Length of wire A = 10 m
Length of wire B = 12 m
Current carried by A= 4 A
Current carried by B = 6 A
Distance between the two parallel wires, r = 0.03 m

Force per unit length acting on the wire,

\frac{F}{l} = \frac{μ_{0} I_{1} I_{2}}{2 πr} {Nm}^{- 1} = \frac{4 π \times 10^{- 7} \times 4 \times 6}{2 π \times 0.03} = 1.6 \times 10^{- 4} {Nm}^{- 1}

Force on 15 cm section of wire B (near its centre),
F= 1.6 x 10^–4 x 0.15 N
= 2.4 x 10^–5 N

The force is repulsive as the currents are in opposite directions; the direction of force is normal to the wire away from A.

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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Moving Charges And Magnetism

Two straight wires A and B of lengths 10 m and 12 m carrying currents of 4.0 A and 6.0 A respectively in opposite directions lie parallel to each other at a distance of 0.03 m. Estimate the force on a 15 cm section of the wire B near its centre.

Some More Questions From Moving Charges And Magnetism Chapter

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