Two identical circular loops P and Q each of | vedclass

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

Question

(D) The magnetic field on the axis of a circular loop of radius $r$ at a distance $x$ from its center is given by $B = \frac{\mu_0 I r^2}{2(r^2 + x^2)

Vedclass · Accepted Answer

$\frac{3\mu_{0}I}{4\sqrt{2}r}$ towards $Q$

Vedclass · Answer

(D) The magnetic field on the axis of a circular loop of radius $r$ at a distance $x$ from its center is given by $B = \frac{\mu_0 I r^2}{2(r^2 + x^2)^{3/2}}$.Here,for both loops $P$ and $Q$,the distance from the center $O$ is $x = r$.Thus,the magnetic field due to loop $P$ $(B_P)$ at $O$ is $B_P = \frac{\mu_0 I r^2}{2(r^2 + r^2)^{3/2}} = \frac{\mu_0 I r^2}{2(2r^2)^{3/2}} = \frac{\mu_0 I r^2}{2(2\sqrt{2}r^3)} = \frac{\mu_0 I}{4\sqrt{2}r}$.Since the current in $P$ is clockwise as seen from $O$,the magnetic field $B_P$ points towards $P$ (away from $Q$).The magnetic field due to loop $Q$ $(B_Q)$ at $O$ is $B_Q = \frac{\mu_0 (4I) r^2}{2(r^2 + r^2)^{3/2}} = \frac{4\mu_0 I r^2}{2(2\sqrt{2}r^3)} = \frac{4\mu_0 I}{4\sqrt{2}r}$.Since the current in $Q$ is also clockwise as seen from $O$,the magnetic field $B_Q$ points towards $Q$ (away from $P$).The net magnetic field $B_{net} = B_Q - B_P = \frac{4\mu_0 I}{4\sqrt{2}r} - \frac{\mu_0 I}{4\sqrt{2}r} = \frac{3\mu_0 I}{4\sqrt{2}r}$ towards $Q$.

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have a common axis. The currents through $P$ and $Q$ are $I$ and $4I$ respectively in the clockwise direction as seen from $O$. The net magnetic field at $O$ is:

Similar Questions

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:

Current $I$ flows through a long conducting wire bent at right angles as shown in the figure. The magnetic field at a point $P$ on the right bisector of the angle $XOY$ at a distance $r$ from $O$ is

The electric current in a circular coil of four turns produces a magnetic induction $32 \ T$ at its centre. The coil is unwound and is rewound into a circular coil of a single turn. If the same current flows through the new coil,the magnetic induction at the centre will be $.......... \ T$.

An equilateral triangle is made by uniform wires $AB, BC, CA$. A current $I$ enters at $A$ and leaves from the midpoint of $BC$. If the length of each side of the triangle is $L$, the magnetic field $B$ at the centroid $O$ of the triangle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module