Question

What is the magnitude of magnetic field at the point P due to a current carrying wire of length 4 m and having a current of 4 A as shown in the figure? $[{\mu }_0=4\pi \times {10}^{-7}Tm/A]$

• A. $10\times {10}^{-8}T$
• B. $11\times {10}^{-8}T$
• C. $9\times {10}^{-8}T$
• D. $5\times {10}^{-8}T$

Answer 1

The correct option is B $11\times {10}^{-8}T$

Magnitude of magnetic field at point P is given by:
$B=\frac{{\mu }_{0}i}{4\pi r}[sin\alpha +sin\beta ]\frac{{\mu }_{0}i}{4\pi \times 5}[sin{30}^{\circ }+sin{60}^{\circ }]B=\frac{4\times 4\pi \times {10}^{-7}}{4\pi \times 5}\times [\frac{1}{2}+\frac{\sqrt{3}}{2}]=4(\sqrt{3}+1)\times {10}^{-8}T=11\times {10}^{-8}T$