An electron moves in a circular orbit with a | vedclass

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

Question

(C) The electric current $i$ produced by an electron moving in a circular orbit of radius $r$ with speed $v$ is given by $i = \frac{ev}{2\pi r}$.The m

Vedclass · Accepted Answer

$\sqrt{v/B}$

Vedclass · Answer

(C) The electric current $i$ produced by an electron moving in a circular orbit of radius $r$ with speed $v$ is given by $i = \frac{ev}{2\pi r}$.The magnetic field $B$ at the centre of the circular current loop is given by $B = \frac{\mu_0 i}{2r}$.Substituting the value of $i$ into the expression for $B$,we get $B = \frac{\mu_0}{2r} \cdot \frac{ev}{2\pi r} = \frac{\mu_0 ev}{4\pi r^2}$.Rearranging the formula to solve for $r^2$,we get $r^2 = \frac{\mu_0 ev}{4\pi B}$.Taking the square root of both sides,we find $r = \sqrt{\frac{\mu_0 ev}{4\pi B}}$.Since $\mu_0$,$e$,and $4\pi$ are constants,the radius $r$ is proportional to $\sqrt{v/B}$.

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to

Similar Questions

The relation between magnetic moment $(M)$ of a current-carrying circular coil and the length $(L)$ of the wire used is:

An electron of charge $e$ moves in a circular orbit of radius $r$ around the nucleus at a frequency $v$. The magnetic moment associated with the orbital motion of the electron is

$A$ closely wound solenoid of $1000$ turns and area of cross-section $2 \times 10^{-4} \ m^2$ carrying a current of $5.0 \ A$. The magnetic moment is . . . . . . $A \ m^2$.

An insulating thin rod of length $l$ has a linear charge density $\rho(x) = \rho_0 \frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second,then the time-averaged magnetic moment of the rod is:

$A$ thin disc of radius $R$ and mass $M$ has charge $q$ uniformly distributed on it. It rotates with angular velocity $\omega$. The ratio of magnetic moment and angular momentum for the disc is

Vedclass Test Series

Exam Paper Generator

Online Exam Module