Question

A long wire bent as shown in the figure carries current I. If radius of the semi-circular portion in 'R', then the magnetic field induction at the point 'O' is:

• A. $\overrightarrow{B}=-\frac{{\mu }_{0}I}{4\pi R}[\pi \hat{k}-2\hat{i}]$
• B. $B=-\frac{{\mu }_{0}I}{4\pi R}|\pi \hat{k}+2\hat{i}|$
• C. $\overrightarrow{B}=\frac{{\mu }_{0}I}{4\pi R}[\pi \hat{k}+2\hat{i}]$
• D. $\overrightarrow{B}=\frac{{\mu }_{0}I}{4\pi R}[\pi \hat{k}-2i]$

Answer 1

The correct option is B $B=-\frac{{\mu }_{0}I}{4\pi R}|\pi \hat{k}+2\hat{i}|$

$\begin{array}{c}\overrightarrow{B}=\frac{{\mu }_{o}i}{4R}\left(-\hat{K}\right)+\frac{{\mu }_{o}i}{4\pi R}\times 2\left(-\hat{i}\right)\\ =\frac{-{\mu }_{o}i}{4\pi R}\left[\pi \hat{K}+2\hat{i}\right]\\ Hence,\\ optionBiscorrectanswer.\end{array}$