Consider two solenoids X and Y such that the | vedclass

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

Question

(B) The magnetic energy $U$ stored in a solenoid is given by $U = \frac{B^2 V}{2 \mu_0}$,where $B$ is the magnetic field,$V$ is the volume,and $\mu_0$

Vedclass · Accepted Answer

$2$ : $1$

Vedclass · Answer

(B) The magnetic energy $U$ stored in a solenoid is given by $U = \frac{B^2 V}{2 \mu_0}$,where $B$ is the magnetic field,$V$ is the volume,and $\mu_0$ is the permeability of free space.Given that the magnetic energy stored in both solenoids is the same,$U_X = U_Y$.Therefore,$\frac{B_X^2 V_X}{2 \mu_0} = \frac{B_Y^2 V_Y}{2 \mu_0}$,which simplifies to $B_X^2 V_X = B_Y^2 V_Y$.Since volume $V = A 	imes L$,we have $B_X^2 A_X L_X = B_Y^2 A_Y L_Y$.Given $A_Y = 2 A_X$ and $L_Y = 2 L_X$,we substitute these into the equation:$B_X^2 A_X L_X = B_Y^2 (2 A_X) (2 L_X)$.$B_X^2 A_X L_X = 4 B_Y^2 A_X L_X$.Dividing both sides by $A_X L_X$,we get $B_X^2 = 4 B_Y^2$.Thus,$\frac{B_X^2}{B_Y^2} = 4$,which implies $\frac{|B_X|}{|B_Y|} = \sqrt{4} = 2$.Therefore,the ratio is $2 : 1$.

Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same,then the ratio of magnitude of magnetic fields of the two solenoids $\frac{|B_X|}{|B_Y|}$ is

Similar Questions

What is a solenoid? Provide information about the magnetic field through a qualitative discussion.

Ampere's circuital law is associated with which law?

The figure shows the cross-sectional view of a hollow cylindrical conductor with inner radius $R$ and outer radius $2R$,carrying a uniformly distributed current $i$ along its axis. The magnetic induction at point $P$ at a distance $3R/2$ from the axis of the cylinder will be

In a toroid,the number of turns per unit length is $1000$ and the current through it is $\frac{1}{4 \pi} \ A$. The magnetic field produced inside (in $Wb/m^2$) will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module