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  • A wire of length l carries current i along the x-axis in a magnetic field which is given by <img alt="\vec{B}= B_0\left ( \hat{i}+\hat{j}+\hat{k} \right )" src="https://entrancecorner.oncodeco

A wire of length l carries current i along the x-axis in a magnetic field which is given by \vec{B}= B_0\left ( \hat{i}+\hat{j}+\hat{k} \right ). Find the magnitude of the magnetic force acting on the wire

Option: 1

B_0il


Option: 2

\sqrt{2} B_{0} i l


Option: 3

2B_0il


Option: 4

\frac{1}{\sqrt 2}B_0il


Answers (1)

best_answer

Force on a current carrying conductor -

\vec{dF} =i (\vec{dl} \times \vec{B})

- wherein

idl=current element 

\overrightarrow{F}= I\left ( \overrightarrow{l}\times \overrightarrow{B} \right )= \overrightarrow{F}=i\left [l (\hat{i})\times B_0(\hat{i}+\hat{j}+\hat{k}) \right ]

\\ \overrightarrow{F}= B_{0}il\left [ \hat{i}\times \left ( \hat{i}+ \hat{j}+\hat{k} \right ) \right ] \\ \Rightarrow \overrightarrow{F}= B_{0}il \left (- \hat{j}+\hat{k} \right ) \\ \Rightarrow {F}=\sqrt{2} B_{0}il

 

Posted by

Suraj Bhandari

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