In the figure shown,there are two semicircles | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The magnetic field at the center of a semicircular arc of radius $r$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{4r}}$.In the given f

Vedclass · Accepted Answer

$\frac{{\mu _0 i}}{4}\left( {\frac{{r_1 + r_2}}{{r_1 r_2}}} \right)$

Vedclass · Answer

(C) The magnetic field at the center of a semicircular arc of radius $r$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{4r}}$.In the given figure,there are two semicircular arcs of radii $r_1$ and $r_2$. The current flows in both arcs such that the magnetic field produced by both at the center $O$ is directed into the plane of the paper (using the right-hand thumb rule).Therefore,the total magnetic induction $B$ at the center $O$ is the sum of the magnetic fields due to both arcs:$B = B_1 + B_2$$B = \frac{{\mu _0 i}}{{4r_1}} + \frac{{\mu _0 i}}{{4r_2}}$$B = \frac{{\mu _0 i}}{4} \left( \frac{1}{r_1} + \frac{1}{r_2} \right)$$B = \frac{{\mu _0 i}}{4} \left( \frac{r_1 + r_2}{r_1 r_2} \right)$Thus,the correct option is $C$.

In the figure shown,there are two semicircles of radii $r_1$ and $r_2$ in which a current $i$ is flowing. The magnetic induction at the centre $O$ will be

Similar Questions

Two circular loops having same radius $[ R = 10 \, cm ]$ and same current $[ I = \frac{7}{2} \, A ]$ are placed along the same axis as shown. If the distance between their centers is $[ 10 \, cm ]$,find the net magnetic field at point $P$ located at the midpoint between them.

The magnetic field at the origin due to a current element $i d l$ placed at a point with vector position $r$ is

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current $I$ and the radius of the circular loop is $r$. The magnetic induction at the center $O$ of the circular loop is:

In the figure,the magnetic induction at the centre $O$ due to the current in the straight portion $AB$ will be:

The magnetic field normal to the plane of a wire coil of $n$ turns and radius $r$ carrying a current $i$ is measured on the axis of the coil at a small distance $h$ from the centre. By what fraction is this field smaller than the field at the centre?

Vedclass Test Series

Exam Paper Generator

Online Exam Module