The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance \(\frac{r}{2}\) from the centre is :
\(\frac{B}{2}\)
- 2B
\((\frac{2}{\sqrt5})^{3B}\)
\((\frac{2}{\sqrt3})^{3B}\)
The Correct Option is C
Solution and Explanation
B=\(\frac{μ_0l}{2r}\)
\(B_a\)=\(\frac{μ_0lr^2}{2(r^2+\frac{r}{4})}\)
⇒\(\frac{B_a}{B}\)=(\(\frac{2}{\sqrt5}\))3
⇒\(B_a\)=(\(\frac{2}{\sqrt5}\))3B
The correct option is (C) : \((\frac{2}{\sqrt5})^{3B}\)
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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.