Question:
An electron having momentum $2.4 \times 10^{-23} \,kg \,ms ^{-1}$ enters a region of uniform magnetic field of $0.15 \,T$. The field vector makes an angle of $30^{\circ}$ with the initial velocity vector of the electron. The radius of the helical path of the electron in the field shall be
An electron having momentum $2.4 \times 10^{-23} \,kg \,ms ^{-1}$ enters a region of uniform magnetic field of $0.15 \,T$. The field vector makes an angle of $30^{\circ}$ with the initial velocity vector of the electron. The radius of the helical path of the electron in the field shall be
Updated On: Jun 14, 2022
- $2\, mm$
- $1 \, mm$
- $\frac{\sqrt{3}}{2} \, mm$
- $0.5 \, mm$
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The Correct Option is D
Solution and Explanation
The radius of the helical path of the electron in the uniform magnetic field is
$r=\frac{m v_{\perp}}{e B}$
$=\frac{m v \sin \theta}{e B}$
$=\frac{\left(2.4 \times 10^{-23}\, kg \,m s ^{-1}\right) \times \sin 30^{\circ}}{\left(1.6 \times 10^{-19} C \right) \times(0.15 T )}$
$=5 \times 10^{-4} m$
$=0.5 \times 10^{-3} m$
$=0.5\, mm$
$r=\frac{m v_{\perp}}{e B}$
$=\frac{m v \sin \theta}{e B}$
$=\frac{\left(2.4 \times 10^{-23}\, kg \,m s ^{-1}\right) \times \sin 30^{\circ}}{\left(1.6 \times 10^{-19} C \right) \times(0.15 T )}$
$=5 \times 10^{-4} m$
$=0.5 \times 10^{-3} m$
$=0.5\, mm$
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.