Question

An infinite current carrying wire,carrying current I is bent in V shape,lying in X-Y plane as shown in figure.Intensity of magnetic field at point P will be
(Take OP = 2a)

• A. $\frac{{\mu }_{0}I}{4\pi a}(2+\sqrt{3})\hat{k}$
• B. $\frac{{\mu }_{0}I}{4\pi a}(2-\sqrt{3})\hat{k}$
• C. $\frac{{\mu }_{0}I}{4\pi a}(2-\sqrt{3})(-\hat{k})$
• D. $\frac{{\mu }_{0}I}{4\pi a}(2+\sqrt{3})(-\hat{k})$

Answer 1

The correct option is A $\frac{{\mu }_{0}I}{4\pi a}(2+\sqrt{3})\hat{k}$

$\text{Solution}:$

Magnetic fiels at P due to wire 1,

$B=\frac{{\mu }_{o}i}{4\pi a}[sin{60}^o+sin{90}^o]\hat{k}$

=$\frac{{\mu }_{o}i}{4\pi a}[\frac{\sqrt{3}}{2}+1]\hat{k}$

Now,

$B_{net}=2B$

$\therefore B_{net}=\frac{{\mu }_{o}i}{4\pi a}[2+\sqrt{3}]\hat{k}$

$\text{Hence A is the correct option}$