Question

An infinite V-shaped wire carrying current I is shown in the adjacent figure. Find the magnitude of magnetic field at point P due to the wire if AP = r.

• A. $\frac{{\mu }_{0}I}{2\pi r}tan\theta$
• B. $\frac{{\mu }_{0}I}{\pi r}tan\left(\frac{\theta }{2}\right)$
• C. $\frac{{\mu }_{0}I}{2\pi r}tan\left(\frac{\theta }{2}\right)$
• D. $\frac{{\mu }_{0}I}{2\pi r}sin\theta$

Answer 1

The correct option is C $\frac{{\mu }_{0}I}{2\pi r}tan\left(\frac{\theta }{2}\right)$

Magnetic field at P due to one section is $B=\frac{{\mu }_{0}I}{4\pi \left(rsin\theta \right)}(1-cos\theta )=\frac{{\mu }_{0}I}{4\pi r}tan\left(\frac{\theta }{2}\right)$

Magnetic field due to both sections $=B_0=2B=\frac{{\mu }_{0}I}{2\pi r}tan\left(\frac{\theta }{2}\right)$