The magnetic field at the centre of a circula | vedclass

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

Question

(C) The magnetic field at the centre of a circular current-carrying coil of radius $r$ is given by:$B_c = \frac{\mu_0 I}{2r} \quad \dots(i)$The magnet

Vedclass · Accepted Answer

$2\sqrt{2}:1$

Vedclass · Answer

(C) The magnetic field at the centre of a circular current-carrying coil of radius $r$ is given by:$B_c = \frac{\mu_0 I}{2r} \quad \dots(i)$The magnetic field on the axis of a circular coil at a distance $x$ from the centre is given by:$B_a = \frac{\mu_0 I r^2}{2(r^2 + x^2)^{3/2}}$Given $x = r$,we substitute this into the formula:$B_a = \frac{\mu_0 I r^2}{2(r^2 + r^2)^{3/2}} = \frac{\mu_0 I r^2}{2(2r^2)^{3/2}} = \frac{\mu_0 I r^2}{2(2\sqrt{2}r^3)} = \frac{\mu_0 I}{4\sqrt{2}r} \quad \dots(ii)$Now,taking the ratio $B_c : B_a$:$\frac{B_c}{B_a} = \frac{\frac{\mu_0 I}{2r}}{\frac{\mu_0 I}{4\sqrt{2}r}} = \frac{4\sqrt{2}r}{2r} = 2\sqrt{2}$Therefore,$B_c : B_a = 2\sqrt{2} : 1$.

The magnetic field at the centre of a circular current-carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c : B_a$ will be

Similar Questions

If you suspect a major deficiency of antibodies in a person,to which of the following would you look for confirmatory evidence?

The middle lamella is primarily composed of:

An ideal refrigerator has a freezer at a temperature of $-13^{\circ}C$. The coefficient of performance of the refrigerator is $5$. The temperature of the air (to which heat is rejected) will be:

$A$ wire elongates by $l \, mm$ when a load $W$ is hung from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$)

An electromagnetic wave of intensity $1400 ~W/m^2$ falls on a metal surface of area $1.5 ~m^2$ and is completely absorbed by it. Find the force exerted by the beam.

Vedclass Test Series

Exam Paper Generator

Online Exam Module