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 \(2 \times 10^{–6} \text{N}\), then the value of x is approximately:
- 1
- 2.4
- 1.4
- 2
The Correct Option is C
Solution and Explanation
\(\frac{dF}{dl}\)=\(2\times10^{−6} N/m\) =\(\frac{µ_0i_1i_2}{2πd}\)
\(2\times10^{−6}=\frac{2\times10^{−7}\times x^2}{0.2}\)
x=\(\sqrt{2}\)≃1.4
So, the correct option is (C): 1.4
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.