An electron in a hydrogen atom revolves aroun | vedclass

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

Question

(D) The magnetic field $B$ at the center of a circular loop carrying current $I$ is given by $B = \frac{\mu_0 I}{2r}$.The current $I$ produced by an e

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(D) The magnetic field $B$ at the center of a circular loop carrying current $I$ is given by $B = \frac{\mu_0 I}{2r}$.The current $I$ produced by an electron revolving with speed $v$ in an orbit of radius $r$ is $I = \frac{ev}{2\pi r}$.Substituting $I$ into the magnetic field formula: $B = \frac{\mu_0}{2r} \left( \frac{ev}{2\pi r} ight) = \frac{\mu_0 ev}{4\pi r^2}$.Given values: $e = 1.6 	imes 10^{-19} \, C$,$v = 6.76 	imes 10^6 \, m/s$,$r = 0.52 	imes 10^{-10} \, m$,and $\frac{\mu_0}{4\pi} = 10^{-7} \, T \cdot m/A$.$B = 10^{-7} 	imes \frac{1.6 	imes 10^{-19} 	imes 6.76 	imes 10^6}{(0.52 	imes 10^{-10})^2}$.$B = 10^{-7} 	imes \frac{10.816 	imes 10^{-13}}{0.2704 	imes 10^{-20}} = 10^{-7} 	imes 40 	imes 10^7 = 40 \, T$.

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^6 \, m/s$ in an orbit of radius $0.52 \, \mathring{A}$. The magnetic field produced at the nucleus of the hydrogen atom is $...... \, T$.

Similar Questions

$A$ coil of $12$ turns is made from a wire of constant length carrying a current $I$. If the number of turns is changed to $3$,what is the percentage change in the magnetic field produced at its centre?

$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $({\mu _0} = 4\pi \times {10^{ - 7}}\,T\cdot m/A)$.

$A$ long straight conductor is bent into the shape as shown. If it carries a current $i$ and the radius of the circular part is $R$,then find the magnetic field $B$ at the centre of the circular coil.

$A$ negative charge is given to a non-conducting loop and the loop is rotated in the plane of paper about its centre as shown in the figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane.

$A$ long straight wire carries a current of $18 \,A$. The magnitude of the magnetic field at a point $12 \,cm$ from it is

Vedclass Test Series

Exam Paper Generator

Online Exam Module