Question

Consider the current carrying loop shown in figure. The magnetic field at $P$ would be:

• A. Zero
• B. $\frac{{\mu }_{0}l}{48r}$ [directed upwards i.e. towards the observer]
• C. $\frac{{\mu }_{0}l}{29r}$ [directed upwards i.e. towards the observer]
• D. $\frac{{\mu }_{0}l}{12r}$ [directed upwards i.e. towards the observer]

Answer 1

The correct option is B $\frac{{\mu }_{0}l}{48r}$ [directed upwards i.e. towards the observer]

$\begin{array}{c}B=\frac{{\mu }_{o}i\left(\frac{\pi }{6}\right)}{4\pi r}-\frac{{\mu }_{o}i\left(\frac{\pi }{6}\right)}{4\pi \left(2r\right)}\\ =\frac{{\mu }_{o}i}{4\pi r}\left[\frac{\pi }{6}-\frac{\pi }{12}\right]\\ =\frac{{\mu }_{o}i}{4\pi r}\left[\frac{\pi }{12}\right]\\ =\frac{{\mu }_{o}i}{48r}towardobserver\\ Hence,\\ optionBiscorrectanswer.\end{array}$