A long, straight wire of radius a carries a c | vedclass

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

Question

(A) Let the total current be $I$ and current density be $J = \frac{I}{\pi a^2}$.
For a point inside the wire at distance $r < a$, using Ampere'

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(A) Let the total current be $I$ and current density be $J = \frac{I}{\pi a^2}$.
For a point inside the wire at distance $r < a$, using Ampere's law: $\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{	ext{enclosed}}$.
$B(2\pi r) = \mu_0 (J \cdot \pi r^2) \Rightarrow B = \frac{\mu_0 J r}{2}$.
At $r = \frac{a}{3}$, $B_A = \frac{\mu_0 J (a/3)}{2} = \frac{\mu_0 J a}{6}$.
For a point outside the wire at distance $r > a$, the wire acts as a long straight wire carrying current $I$ at its axis.
$B(2\pi r) = \mu_0 I = \mu_0 (J \pi a^2) \Rightarrow B = \frac{\mu_0 J a^2}{2r}$.
At $r = 2a$, $B_B = \frac{\mu_0 J a^2}{2(2a)} = \frac{\mu_0 J a}{4}$.
The ratio is $\frac{B_A}{B_B} = \frac{\mu_0 J a / 6}{\mu_0 J a / 4} = \frac{4}{6} = \frac{2}{3}$.

$A$ long, straight wire of radius $a$ carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distances $\frac{a}{3}$ and $2a$ respectively from the axis of the wire is:

Similar Questions

$A$ solenoid of length $0.5 \ m$ has a radius of $1 \ cm$ and is made up of $250$ turns. It carries a current of $5 \ A$. What is the magnitude of the magnetic field inside the solenoid?

If the number of turns per unit length of a solenoid is doubled, what happens to the magnetic field in the solenoid?

What is the magnetic field at point $P$ located at a distance of $\frac{3R}{2}$ from the center of the cylindrical conductor with inner radius $R$ and outer radius $2R$ carrying a current $i$?

$A$ current $i$ ampere flows along an infinitely long straight thin-walled tube. The magnetic induction at any point inside the tube is:

The magnetic induction along the axis of a toroidal solenoid is independent of

Vedclass Test Series

Exam Paper Generator

Online Exam Module