Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10–6 N, then the value of x is approximately:
- 1
- 2.4
- 1.4
- 2
The Correct Option is C
Solution and Explanation
To solve this problem, we need to determine the value of current \( x \) for two long, parallel wires that are 0.20 m apart and carry the same current in the same direction. The force of attraction per meter between the wires is given as \(2 \times 10^{-6} \, \text{N/m}\).
The formula for the force per unit length between two parallel current-carrying wires is given by:
\(F = \frac{\mu_0 \cdot I_1 \cdot I_2}{2\pi \cdot d}\)
where:
- \(\mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}\), is the permeability of free space.
- \(I_1\) and \(I_2\) are the currents through the wires, both are equal to \(x\) A.
- \(d = 0.20 \, \text{m}\), is the distance between the wires.
Since the currents are the same and in the same direction, we can write:
\(F = \frac{4\pi \times 10^{-7} \cdot x^2}{2\pi \cdot 0.20}\)
This simplifies to:
\(F = \frac{2 \times 10^{-7} \cdot x^2}{0.20}\)
Setting this equal to the given force per unit length:
\(\frac{2 \times 10^{-7} \cdot x^2}{0.20} = 2 \times 10^{-6}\)
Simplifying gives:
\(x^2 = \frac{2 \times 10^{-6} \cdot 0.20}{2 \times 10^{-7}}\)
\(x^2 = 2 \end{equation}\)
Solving for \(x\), we get:
\(x = \sqrt{2} = 1.414\ldots\)
Rounding to a single decimal place, the approximate value of \(x\) is \(1.4\). Thus, the correct answer is 1.4.
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Concepts Used:
Magnetic Force
Magnetic force is the attraction or repulsion force that results from the motion of electrically charged particles. The magnets are attracted or repellent to one another due to this force. A compass, a motor, the magnets that hold the refrigerator door, train tracks, and modern roller coasters are all examples of magnetic power.
A magnetic field is generated by all moving charges, and the charges that pass through its regions feel a force. Depending on whether the force is attractive or repulsive, it may be positive or negative. The magnetism force is determined by the object's charge, velocity, and magnetic field.
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