SATHEE: moving-charges-and-magnetism Question 25

moving-charges-and-magnetism Question 25

Question: Q. 1. Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.

R [O.D. I, II, III 2017]

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Solution:

Ans. (i) For directions of $\vec{E}, \vec{B}, \vec{v}$

(ii) For magnitudes of $\vec{E}, \vec{B}, \vec{v}$

(i) The velocity $\vec{v}$ of the charged particles, and the $\vec{E}$ and $\vec{B}$ vectors, should be mutually perpendicular. $1 / 2$ Also the forces on $q$ , due to $\vec{E}$ and $\vec{B}$ must be oppositely directed. (Also accept if the student draws a diagram to show the directions.)

(ii) $q E = q v B$

$1 / 2$

$v = \frac{E}{B}$

$1 / 2$

[Alternatively, The student may write :

Force due to electric field $= q \vec{E}$

Force due to magnetic field $= q (\vec{v} \times \vec{B})$

The required condition is

$\begin{aligned} q \vec{E} & = - q (\vec{v} \times \vec{B}) [or \vec{E} & = - (\vec{v} \times \vec{B}) = (\vec{B} \times \vec{v})] \end{aligned}$

(Note : Award 1 mark only if the student just writes :

“The forces, on the charged particle, due to the electric and magnetic fields, must be equal and opposite to each other”)

[CBSE Marking Scheme 2017]

Detailed Answer :

If a charged particle travels in crossed electric and magnetic field, then both fields are perpendicular to each other.

Force on the particle will be :

$\begin{aligned} \vec{F} = \vec{F_{E}} + \vec{F_{B}} & \vec{F} = \vec{q E} + q (\vec{v} \times \vec{B}) \end{aligned}$

As $F_{B}$ is $180^{\circ}$ to $F_{E}$ , so

$\begin{aligned} \vec{F} = \vec{q E} - q (\vec{v} \times \vec{B}) & \vec{F} = q (E - v_{v} B) \hat{j} \end{aligned}$

Now to select a particle, making resultant force as zero, hence

Now,

$0 = q (E - v B) \hat{j}$

Hence,

$\begin{aligned} E - v B & = 0 E & = v B \end{aligned}$

Hence,

$v = \frac{E}{B}$

Moving Charges And Magnetism

moving-charges-and-magnetism Question 25

Detailed Answer :

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Moving Charges And Magnetism

moving-charges-and-magnetism Question 25

Detailed Answer :

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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