Question:
A plane metallic sheet is placed with its face parallel to lines of magnetic induction $B$ of a uniform field. A particle of mass $m$ and charge $q$ is projected with a velocity $v$ from a distance $d$ from the plane normal to the lines of induction. Then, the maximum velocity of projection for which the particle does not hit the plate is :
A plane metallic sheet is placed with its face parallel to lines of magnetic induction $B$ of a uniform field. A particle of mass $m$ and charge $q$ is projected with a velocity $v$ from a distance $d$ from the plane normal to the lines of induction. Then, the maximum velocity of projection for which the particle does not hit the plate is :
Updated On: Jul 12, 2022
- $ \frac{2Bqd}{m} $
- $ \frac{Bqd}{m} $
- $ \frac{Bqd}{2m} $
- $ \frac{Bqm}{d} $
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The Correct Option is B
Solution and Explanation
The charged particle bends in a circle of radius $r$
$B q v \sin \frac{\pi}{2} =\frac{m v^{2}}{r}$
$\Rightarrow r =\frac{m v}{B q}$
The particle does not hit the plate if
$r \leq d$
or $\frac{m v}{B q} \leq d$
or $v \leq \frac{B q d}{m}$
$\therefore v_{\max } =\frac{B q d}{m}$
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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.