A rod of length l is rotating with constant a | vedclass

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

Question

(A) The potential difference $V$ between two points at distances $x_1$ and $x_2$ from the axis of rotation is given by the formula:$V = \frac{1}{2} B

Vedclass · Accepted Answer

in increasing arithmetic progression.

Vedclass · Answer

(A) The potential difference $V$ between two points at distances $x_1$ and $x_2$ from the axis of rotation is given by the formula:$V = \frac{1}{2} B \omega (x_2^2 - x_1^2)$Let the spacing between consecutive points be $d$. Then the points are at distances $0, d, 2d, 3d, \dots, 8d$ from the origin.The potential difference between consecutive points $n$ and $(n-1)$ is:$V_n = \frac{1}{2} B \omega [ (nd)^2 - ((n-1)d)^2 ]$$V_n = \frac{1}{2} B \omega d^2 [ n^2 - (n^2 - 2n + 1) ]$$V_n = \frac{1}{2} B \omega d^2 (2n - 1)$For $n = 1, 2, 3, \dots, 8$,the potential differences are proportional to $(2(1)-1), (2(2)-1), (2(3)-1), \dots$,which are $1, 3, 5, 7, \dots$.This sequence $1, 3, 5, 7, \dots$ is an arithmetic progression with a common difference of $2$.

Similar Questions

$A$ square loop $ABCD$ is moving with constant velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ which is perpendicular to the plane of paper and directed outward. The resistance of the coil is $R$. What is the rate of production of heat energy in the loop? [$L$ = length of side of the loop]

$A$ square conducting frame of side $a$ and a long straight wire carrying current $I$ are placed as shown in the figure. If the frame is moved to the right with a constant velocity $V$,then the induced $emf$ in the frame is proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module