A current carrying circular coil of radius R | vedclass

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

Question

(A) The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B_2 = \frac{\mu_0 I}{2R}$.The magnetic field a

Vedclass · Accepted Answer

$R \sqrt{3}$

Vedclass · Answer

(A) The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B_2 = \frac{\mu_0 I}{2R}$.The magnetic field at an axial point $P$ at a distance $x$ from the centre is given by $B_1 = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$.Given $B_1 = \frac{B_2}{8}$,we substitute the expressions:$\frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} = \frac{1}{8} 	imes \frac{\mu_0 I}{2R}$.Simplifying the equation:$\frac{R^2}{(R^2 + x^2)^{3/2}} = \frac{1}{8R}$.$8R^3 = (R^2 + x^2)^{3/2}$.Taking the power of $2/3$ on both sides:$(8R^3)^{2/3} = R^2 + x^2$.$4R^2 = R^2 + x^2$.$x^2 = 3R^2$.$x = R \sqrt{3}$.

$A$ current carrying circular coil of radius $R$ produces magnetic fields $B_1$ and $B_2$ at an axial point $P$ at a distance $x$ from its centre and at a point $Q$ placed at its centre respectively. If $B_1 = \frac{B_2}{8}$,the value of $x$ is

Similar Questions

$A$ current of $1 \, A$ flows through an infinitely long straight wire. The magnetic field produced at a point $1 \, m$ away from it is:

What is the ratio of the magnetic field at the center of a circular ring of radius $R$ to the magnetic field at a point on its axis at a distance of $3R$ from the center?

$A$ long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from the axis of the wire is:

$PQRS$ is a square loop made of a uniform conducting wire. The current enters the loop at $P$ and leaves at $S$. Then the magnetic field will be

The correct Biot-Savart law in vector form is

Vedclass Test Series

Exam Paper Generator

Online Exam Module