Question

The magnetic field at a point O distance r from the corner of an infinitely long wire carrying a current $I$ and bent at right angle is

• A. $\frac{{\mu }_{0}I}{4\pi }$
• B. $\frac{{\mu }_{0}I}{\pi r}$
• C. $\frac{{\mu }_{0}I}{4\pi r}$
• D. $zero$

Answer 1

Answer: (A)

$\frac{{\mu }_{0}I}{4\pi }$

Given : The magnetic field at a point O distance r from the corner of an infinitely long wire carrying a current II and bent at right angle is

Solution:

Point O lies on the axis of one wire so magnetic field due to wire will be 0.

Point O is at a distance r from another wire

We have a formula for magnetic field due to wire as B=$\frac{\mu I}{4\pi r}\times (sin{\theta }_1+sin{\theta }_2)$

Where ${\theta }_{1}and{\theta }_2$are angle made from point to the ends of wire.

In condition of another wire one end is at infinity so angle will be ${90}^0$ and another end is front of point O so angle will be $0^0$.

So net magnetic field B=$\frac{\mu I}{4\pi r}\times (sin90+sin0)$ $\Rightarrow$ B= $\frac{\mu I}{4\pi r}$

The correct Opt=C