An electron in a circular orbit of radius 0.0 | vedclass

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

Question

(D) Given:Radius $r = 0.05 \ nm = 0.05 	imes 10^{-9} \ m$Frequency $f = 10^{16} \ Hz$ (revolutions per second)Charge of electron $e = 1.6 	imes 10^{

Vedclass · Accepted Answer

$1.26 	imes 10^{-23}$

Vedclass · Answer

(D) Given:Radius $r = 0.05 \ nm = 0.05 	imes 10^{-9} \ m$Frequency $f = 10^{16} \ Hz$ (revolutions per second)Charge of electron $e = 1.6 	imes 10^{-19} \ C$The magnetic moment $M$ of a current loop is given by $M = I 	imes A$, where $I$ is the current and $A$ is the area of the loop.The current $I$ due to the revolving electron is $I = e 	imes f$.The area of the circular orbit is $A = \pi r^{2}$.Substituting these into the formula for magnetic moment:$M = (e 	imes f) 	imes (\pi r^{2})$$M = (1.6 	imes 10^{-19} \ C) 	imes (10^{16} \ s^{-1}) 	imes (3.14) 	imes (0.05 	imes 10^{-9} \ m)^{2}$$M = 1.6 	imes 10^{-19} 	imes 10^{16} 	imes 3.14 	imes 0.0025 	imes 10^{-18}$$M = 1.6 	imes 3.14 	imes 0.0025 	imes 10^{-21} \ m^{2} \cdot C/s$$M = 0.01256 	imes 10^{-21} \ A \ m^{2}$$M = 1.26 	imes 10^{-23} \ A \ m^{2}$

An electron in a circular orbit of radius $0.05 \ nm$ performs $10^{16}$ revolutions per second. The magnetic moment due to this rotation of the electron is (in $A \ m^{2}$):

Similar Questions

Derive an expression for the torque acting on a current-carrying loop suspended in a uniform magnetic field.

The unit of magnetic moment is

$A$ charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to the normal axis,then the magnetic moment of the loop is:

Two wires of the same length are shaped into a square and a circle. If they carry the same current,the ratio of their magnetic moments is:

$A$ closely wound solenoid of $800$ turns and area of cross-section $2.5 \times 10^{-4} \; m^2$ carries a current of $3.0 \; A$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

Vedclass Test Series

Exam Paper Generator

Online Exam Module