Question:
The magnetic field at the center of current carrying circular loop is \(B_1\). The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is \(B_2\). The value of \(B_1/B_2\) will be
The magnetic field at the center of current carrying circular loop is \(B_1\). The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is \(B_2\). The value of \(B_1/B_2\) will be
Updated On: Sep 17, 2024
- 9 : 4
- 12 : √5
- 8 : 1
- 5 : √3
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The Correct Option is C
Solution and Explanation
\(B_1 = \frac{μ0I}{2R}\)
\(B_2 = \frac{μ0IR^2}{2(R^2 + 3R^2)^{3/2} }= \frac{1}{8}(\frac{ μ0I}{2R}) = \frac{B_1}{8}\frac{B_1}{B_2} = \frac{8}{1}\)
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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.