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>B</mi> </mrow> </mrow> <mo>⃗</mo> </mover> <mo>=</mo> <msub> <mrow> <mrow> <mi>B</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:

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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 $\vec{B} = B_{0} \hat{i}$ 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 -

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

12 Views | Posted 4 months ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 months ago

Correct Option - 3

Detailed Solution:

Since magnetic force cannot change the speed. So only electric field which is along -direction will change the speed along -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 <img src="file:///C:/Users/ALOK~1.SIN/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" width="8" height="17">-direction will change the speed along <img src="file:///C:/Users/ALOK~1.SIN/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png" width="10" height="17">-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>   <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> <div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753781981phpInHABY.jpeg" alt="" width="323" height="231" 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> </div><div> <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> </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 $\vec{B} = B_{0} \hat{i}$ 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 B ⃗ = B 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 $\vec{B} = B_{0} \hat{i}$ act on the particle, its speed will double after a time: