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 3 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

3 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>

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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:

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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:

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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: