An electron revolves in a circle of radius $0.4 \mathring{A}$ with a speed of $10^5 ms^{-1}. $ The magnitude of the magnetic field, produced at the centre of the circular path due to the motion of the electron, in $Wb \, \, m^{-2} $ is
- 0.01
- 10
- 1
- 0.005
The Correct Option is C
Solution and Explanation
$\hspace20mm B= \frac {\mu _0qv}{4 \pi r^2} $
Given $\frac {\mu_0}{4 \pi}=10^{-7}, q=1.6 \times 10^{-19}C,$
$\hspace20mm v=10^5ms^{-1} $
$\hspace20mm r=0.4 \mathring{A}=0.4 \times 10^{-10}m$
$\therefore \hspace20mm B=10^{-7}\times \frac {1.6 \times 10^{-19}\times 10^5}{(0.4 \times 10^{-10})^2}=1 \, Wb \, m^{-2} $
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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.