A particle of mass <math> <mi>m</mi> </math> and charge <math> <mi>q</mi> </math> has an initial velocity <math> <mover accent="true"> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> . If an electric field <math> <mover accent="true"> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> and magnetic field <math> <mover accent="true"> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> act on the particle, its speed will double after a time:

Since magnetic force cannot change the speed. So only electric field which is along x -direction will change the speed along X -direction only. v x = E 0 q m t but v y = v 0 <!- [endif]-><!- [endif]-> 2 v 0 = v x 2 + v y 2 <!- [endif]-><!- [endif]-> 4 v 0 2 = E o 2 q 2 t 2 m 2 + v 0 2 <!- [endif]-><!- [endif]-> t = 3 m v o q E o <!- [endif]-><!- [endif]->

A particle of mass <math> <mi>m</mi> </math> and charge <math> <mi>q</mi> </math> has an initial velocity <math> <mover accent="true"> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> . If an electric field <math> <mover accent="true"> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> and magnetic field <math> <mover accent="true"> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> </math> &nbsp;act on the particle, its speed will double after a time:

Ask & Answer Question

Physics Class 12th Physics Moving Charges and Magnetism

A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v} = v_{0} \hat{j}$ . If an electric field $\vec{E} = E_{0} \hat{i}$ and magnetic field $\vec{E} = E_{0} \hat{i}$ act on the particle, its speed will double after a time:

Option 1 -

$\frac{2 m v_{0}}{q E_{0}}$

Option 2 -

$\frac{\sqrt[]{2} m v_{0}}{q E_{0}}$

Option 3 -

$\frac{\sqrt[]{3} m v_{0}}{q E_{0}}$

Option 4 -

$\frac{3 m v_{0}}{q E_{0}}$

6 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

Since magnetic force cannot change the speed. So only electric field which is along $x$ -direction will change the speed along $X$ -direction only.

$v_{x} = \frac{E_{0} q}{m} t$ but $v_{y} = v_{0}$

$2 v_{0} = \sqrt[]{v_{x}^{2} + v_{y}^{2}}$

$4 v_{0}^{2} = \frac{E_{o}^{2} q^{2} t^{2}}{m^{2}} + v_{0}^{2}$

$t = \frac{\sqrt[]{3} m v_{o}}{q E_{o}}$

Since magnetic force cannot change the speed. So only electric field which is along <math> <mi>x</mi> </math> -direction will change the speed along <math> <mi>X</mi> </math> -direction only. <math> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>q</mi> </mrow> </mrow> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> </mfrac> <mi>t</mi> </math> but <math> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>y</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> <!- [endif]-><!- [endif]-> <math> <mn>2</mn> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <mrow> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>+</mo> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>y</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </mrow> </mrow> <mrow></mrow> </mroot> </math> <!- [endif]-><!- [endif]-><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755759613phpuS3Iui.jpeg" alt="" width="363" height="254" loading="lazy"></picture></div><div> <math> <mn>4</mn> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <mrow> <msubsup> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <msup> <mrow> <mrow> <mi>q</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <msup> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>+</mo> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> <!- [endif]-><!- [endif]-> <math> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mi>m</mi> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mi>q</mi> <msub> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> <!- [endif]-><!- [endif]-></div></div>

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
682k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v} = v_{0} \hat{j}$ . If an electric field $\vec{E} = E_{0} \hat{i}$ and magnetic field $\vec{E} = E_{0} \hat{i}$ act on the particle, its speed will double after a time:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

A particle of mass m and charge q has an initial velocity v ⃗ = v 0 j ˆ . If an electric field E ⃗ = E 0 i ˆ and magnetic field E ⃗ = E 0 i ˆ act on the particle, its speed will double after a time:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v} = v_{0} \hat{j}$ . If an electric field $\vec{E} = E_{0} \hat{i}$ and magnetic field $\vec{E} = E_{0} \hat{i}$ act on the particle, its speed will double after a time: