SATHEE: moving-charges-and-magnetism Question 16

moving-charges-and-magnetism Question 16

Question: Q. 9. Consider the motion of a charged particle of mass $m$ and charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ .

(i) If $\vec{v}$ is perpendicular to $\vec{B}$ , show that it describes a circular path having angular frequency

$\to ω = q B / m$ .

(ii) If the velocity $\vec{v}$ has a component parallel to the magnetic field $\vec{B}$ , trace the path described by the particle. Justify your answer.

U] [Delhi Comptt. I, II, III 2014]

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Solution:

Ans. (i) Force acting on the charged particle, moving with a velocity $\vec{v}$ , in a magnetic field $\vec{B}$ :

$\vec{F} = q (\vec{v} \times \vec{B})$

As, $\vec{v} ⊥ \vec{B}, F = q v B$

Since, $\vec{F} ⊥ \vec{v}$ , it acts as a centripetal force and makes the particle move in a circular path in the plane, perpendicular to the magnetic field.

$∴ q v B = \frac{m v^{2}}{r}$

$∴ r = \frac{m v}{q B}$ or $\frac{v}{r} = \frac{q B}{m}$

Now

$ω = \frac{v}{r}$

$ω = \frac{q B}{m}$

(ii)

The component of velocity $\vec{v}$ parallel to magnetic field, will make the particle move along the field.

The perpendicular component of velocity $\vec{v}$ will cause the particle to move along a circular path in the plane perpendicular to the magnetic field. Hence, the particle will follow a helical path, as shown.

[CBSE Marking Scheme, 2014] 1

Moving Charges And Magnetism

moving-charges-and-magnetism Question 16

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Moving Charges And Magnetism

moving-charges-and-magnetism Question 16

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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