Question:
A helium nucleus makes full rotation in a circle of
radius 0.8 min 2 s. The value of'magnetic field B at the
centre of the circle, will be $(\mu _0=$ permeability constant)
A helium nucleus makes full rotation in a circle of
radius 0.8 min 2 s. The value of'magnetic field B at the
centre of the circle, will be $(\mu _0=$ permeability constant)
Updated On: Jul 5, 2022
- $\frac {2 \times 10^{-19}}{\mu _0} $
- $2 \times 10^{-19} \mu _0 $
- $10^{-19} \mu _0 $
- $\frac {10^{-19}}{\mu_0} $
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The Correct Option is C
Solution and Explanation
The magnetic field at the centre of a circle is given by
$\hspace15mm B=\frac {\mu _0i}{2r} $
where, i is current and r the radius of circle.
Also, $\hspace15mm i= \frac {q}{t}$
For helium nucleus, q = 2e
$\therefore \hspace15mm i= \frac {2e}{t} $
So, $\hspace15mm B= \frac {\mu _0.2e}{2rt} $
$\hspace15mm = \frac {\mu _0 \times 2 \times 1.6 \times 10^{-19}}{2 \times 0.8 \times 2} $
$\hspace15mm = 10^{-19}\mu _0 $
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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.