Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Two long parallel conductors and <img alt="\mathrm{S_{2}}" src="https://entrancecorner.on

Two long parallel conductors \mathrm{S_{1}} and \mathrm{S_{2}} are separated by a distance \mathrm{10 \mathrm{~cm}} and carrying currents of \mathrm{4 \mathrm{~A} \, and\, 2 \mathrm{~A}} respectively. The conductors are placed along \mathrm{x-} axis in \mathrm{\mathrm{X}-\mathrm{Y}} plane. There is a point \mathrm{\mathrm{P}} located between the conductors (as shown in figure).
A charge particle of \mathrm{3 \pi} coulomb is passing through the point \mathrm{\mathrm{P}} with velocity \vec{v}\mathrm{=(2 \hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s}}; where \mathrm{\hat{i}_{i} \& \hat{j}} represents unit vector along \mathrm{x\, \& \, y} axis respectively.
The force acting on the charge particle is \mathrm{4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) N}. The value of \mathrm{x} is :

Option: 1

2


Option: 2

1


Option: 3

3


Option: 4

-3


Answers (1)

best_answer


Charge particle will experience a force due to magnetic field produced by current-carrying wired using Lorentz force equation
\vec{F}= q\left ( \vec{v} \times \vec{B}\right )

To calculate the magnetic field at 'P'
{\vec{B}}=\mathrm{ B_{1}\left ( -\hat{k} \right )+B_{2}\hat{k}}
     \mathrm{= \frac{\mu _{0}\times 4}{2\pi\times 4\times 10^{-2}}\left ( -\hat{k} \right )+\frac{\mu _{0}\times 2}{2\pi\times 6\times 10^{-2}}\left ( \hat{k} \right )}
      \mathrm{= \frac{\mu _{0}}{\pi}\times 10^{2}\left [ \frac{-1}{2}+\frac{1}{6} \right ]\hat{k}}
  \vec{B}\mathrm{= \frac{\mu _{0}}{3\pi}\times 10^{2}\left ( -\hat{k} \right )}

 \vec{F}\mathrm{=3\pi\left [ \left ( 2\hat{i} +3\hat{j}\right )\times \left ( \frac{\mu _{0}}{3\pi}\times 10^{+2} \right ) \left ( -\hat{k} \right )\right ]}
       \mathrm{=10^{+2}\times \mu _{0}\left [ 2\hat{j}-3\hat{i} \right ]}
       \mathrm{=4\pi\times 10^{-7}\times 10^{2}\left [ 2 \hat{j}-3\hat{i} \right ]}
       \mathrm{=4\pi\times 10^{-5}\times \left [ -3 \hat{i}+2\hat{j} \right ]}
     \mathrm{x=3}

The correct answer is (3)   

Posted by

Gautam harsolia

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: Most important chapters for physics, chemistry, mathematics to score good marks
anam-khan

JEE Main 2025 session 2 dates clash with ISC, PSEB 12th exams; no impact on major science subjects
anam-khan

Delhi police EOW books FIITJEE for fraud; 192 complaints filed

Latest Question