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

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(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

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in increasing arithmetic progression.

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(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 $2$.

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