Two long parallel straight conductors separated by a distance of 0.20\text{ m} in vacuum c… — JAMB UTME

Two long parallel straight conductors separated by a distance of $0.20\text{ m}$ in vacuum carry steady currents of $5.0\text{ A}$ and $8.0\text{ A}$ in opposite directions. Given that the permeability of free space $\mu_0 = 4\pi \times 10^{-7}\text{ T}\cdot\text{m/A}$ , what is the magnitude of the magnetic force per unit length acting between the conductors and the nature of this force?

$4.0 \times 10^{-5}\text{ N/m}$ , repulsiveAnswer
B
$4.0 \times 10^{-5}\text{ N/m}$ , attractive
C
$8.0 \times 10^{-5}\text{ N/m}$ , repulsive
D
$2.0 \times 10^{-5}\text{ N/m}$ , attractive

Answer

4.0 \times 10^{-5}\text{ N/m}

, repulsive

Applying the formula for force per unit length gives

\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{(4\pi \times 10^{-7})(5.0)(8.0)}{2\pi (0.20)} = 4.0 \times 10^{-5}\text{ N/m}

. Since the currents flow in opposite directions, the magnetic interaction is repulsive.

Step-by-Step Solution

Identify given variables and the formula for force per unit length between parallel conductors.

Given:

I_1 = 5.0\text{ A}

I_2 = 8.0\text{ A}

d = 0.20\text{ m}

\mu_0 = 4\pi \times 10^{-7}\text{ T}\cdot\text{m/A}

. Formula:

\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}

The magnetic force per unit length between two parallel wires depends on the current magnitudes and their distance of separation.

Substitute values into the equation and compute the magnitude.

\frac{F}{L} = \frac{(4\pi \times 10^{-7})(5.0)(8.0)}{2\pi (0.20)} = \frac{2 \times 10^{-7} \times 40}{0.20} = 4.0 \times 10^{-5}\text{ N/m}

Canceling

4\pi

with

2\pi

yields a multiplier of

2 \times 10^{-7}

, simplifying numerical computation.

Determine the direction of force based on current flow direction.

The force is repulsive.

Parallel conductors carrying currents in opposite directions generate magnetic field configurations that force the wires apart.

Key Concept

Magnetic force per unit length between parallel current-carrying conductors

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