Question:
An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude
An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude
Updated On: Jul 13, 2024
- $\frac{\mu_0 n^2 e}{r}$
- $\frac{\mu_0 n e}{2r}$
- $\frac{\mu_0 n e}{2 \pi r}$
- Zero
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The Correct Option is B
Solution and Explanation
Current in the orbit, $I=\frac{e}{T}$
$I=\frac{e}{(2 \pi/{\omega})}=\frac{\omega e}{2 \pi}=\frac{(2 \pi n)e}{2 \pi}=ne$
Magnetic field at centre of current carrying circular
coil is given by
$ \, \, \, \, B=\frac{\mu_0 I}{2r}=\frac{\mu_0 ne}{2r}$
$I=\frac{e}{(2 \pi/{\omega})}=\frac{\omega e}{2 \pi}=\frac{(2 \pi n)e}{2 \pi}=ne$
Magnetic field at centre of current carrying circular
coil is given by
$ \, \, \, \, B=\frac{\mu_0 I}{2r}=\frac{\mu_0 ne}{2r}$
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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.