Question

A wire carries a steady current of $50\text{A}$ as shown in the figure. Find the magnetic field caused by segment $AB$ of length $1\text{cm}$ of the wire at a point $P$ where $OP=1\text{m}$.

• A. $30\text{nT}⨂$
• B. $50\text{nT}⨂$
• C. $30\text{nT}⨀$
• D. $50\text{nT}⨀$

Answer 1

The correct option is C $30\text{nT}⨀$

Since the length of the element is very small as compared, the distance between the point $P$ and the wire. So, we can use Biot-Savart law to calculate the magnetic field at point $P$. Thus,

$B_P=\frac{{\mu }_0}{4\pi }\frac{il\sin \theta }{r^2}$

$={10}^{-7}\times \frac{50\times 0.01\times \sin {37}^{\circ }}{1^2}=3\times {10}^{-8}\text{T}=30\text{nT}$

From right-hand thumb rule, the direction of magnetic field is outwards of the plane.