(C) The relationship between force $F$ and potential energy $U$ is given by $F = - \frac{dU}{dr}$.Given $U = - \frac{ke^2}{3r^3} = - \frac{ke^2}{3} r^

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(C) The relationship between force $F$ and potential energy $U$ is given by $F = - \frac{dU}{dr}$.Given $U = - \frac{ke^2}{3r^3} = - \frac{ke^2}{3} r^{-3}$.Now,differentiating $U$ with respect to $r$:$F = - \frac{d}{dr} \left( - \frac{ke^2}{3} r^{-3} \right)$$F = \frac{ke^2}{3} \frac{d}{dr} (r^{-3})$$F = \frac{ke^2}{3} (-3 r^{-4})$$F = - \frac{ke^2}{r^4}$.

Class 12 Physics Electric Potential and Capacitance Relation between Electric Field and Potential and Potential Gradient

Medium

If the potential energy of an electron and a proton at a distance $r$ is given by the formula $U = - \left( \frac{ke^2}{3r^3} \right)$,then which law of force applies?

A
$F = \frac{ke^2}{r^2}$
B
$F = - \frac{3}{4} \frac{ke^2}{r^4}$
C
$F = - \frac{ke^2}{r^4}$
D
$F = \frac{ke^2}{r}$

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Class 12 Questions

Class 12

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Chapter

Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

Due to some charges on the $x$-axis,the potential at a point on the $x$-axis is given by $V(x) = 20/(x^2 - 4) \ V$. The electric field at $x = 4 \ \mu m$ is given by:

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The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

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In which region is the magnitude of the $x$-component of the electric field maximum,if the potential $(V)$ versus distance $(X)$ graph is as shown?

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If $V$ is the electric potential at a given point,then the electric field $E_x$ in the $x$-direction at that point is:

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Electric field in a region is given by $\vec{E} = Ax\hat{i} + By\hat{j}$, where $A = 10 \ V/m^2$ and $B = 5 \ V/m^2$. If the electric potential at a point $(10, 20)$ is $500 \ V$, then the electric potential at the origin is . . . . . . $V$.

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If the potential energy of an electron and a proton at a distance $r$ is given by the formula $U = - \left( \frac{ke^2}{3r^3} \right)$,then which law of force applies?

Similar Questions

Due to some charges on the $x$-axis,the potential at a point on the $x$-axis is given by $V(x) = 20/(x^2 - 4) \ V$. The electric field at $x = 4 \ \mu m$ is given by:

The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

In which region is the magnitude of the $x$-component of the electric field maximum,if the potential $(V)$ versus distance $(X)$ graph is as shown?

If $V$ is the electric potential at a given point,then the electric field $E_x$ in the $x$-direction at that point is:

Electric field in a region is given by $\vec{E} = Ax\hat{i} + By\hat{j}$, where $A = 10 \ V/m^2$ and $B = 5 \ V/m^2$. If the electric potential at a point $(10, 20)$ is $500 \ V$, then the electric potential at the origin is . . . . . . $V$.

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