Question:
In the hydrogen atom, the electron is making $6.6 \times 10^{15}$ rps. If the radius of orbit is $0.53 \times 10^{-10}$ m, then magnetic field produced at the centre of the orbit is
In the hydrogen atom, the electron is making $6.6 \times 10^{15}$ rps. If the radius of orbit is $0.53 \times 10^{-10}$ m, then magnetic field produced at the centre of the orbit is
Updated On: Apr 15, 2024
- 140T
- 12.5T
- 1.4T
- 0.14T
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The Correct Option is B
Solution and Explanation
Current, $i=q v$
$B=\frac{\mu_{0} i}{2 r}=\frac{\mu_{0} q v}{2 r}$
$=\frac{4 \pi \times 10^{-7} \times 1.6 \times 10^{-19} \times 6.6 \times 10^{15}}{2 \times 0.53 \times 10^{-10}}$
$=\frac{2 \pi \times 1.6 \times 6.6}{5.3}=12.513\, T$
$B=\frac{\mu_{0} i}{2 r}=\frac{\mu_{0} q v}{2 r}$
$=\frac{4 \pi \times 10^{-7} \times 1.6 \times 10^{-19} \times 6.6 \times 10^{15}}{2 \times 0.53 \times 10^{-10}}$
$=\frac{2 \pi \times 1.6 \times 6.6}{5.3}=12.513\, T$
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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.