Relation between Field and Potential

The potential at a point $x$ due to some charge is given by equation $V\left(x\right)=\frac{20}{(x^2-4)}$ volts. Then electric field at $x=4$ is given by

What is angle between electric field and equipotential surface?

An electron at rest is accelerated through a potential difference of $200 \mathrm{V}.$ If the electron acquires a velocity of $8.4\times {10}^{\mathrm{8 }}\mathrm{c}\mathrm{m}/\mathrm{s},$ its $\frac{e}{m}$ ratio is

A uniform electric field is prevailing in $X$ -direction in certain region. The co-ordinates of points P, Q and R are (0, 0), (2, 0) and (0, 2) respectively. Which of the following alternatives is true for the potentials at these points?

Electric field in a region is given by $E=\left(\frac{M}{x^3}\right)\widehat{i}$ , then the correct expression for the potential in the region is (assume potential at infinity is zero).

From a point charge, there is a fixed point A. At A, there is an electric field of $500 V/m$ and potential difference of 3000V. Distance between point charge and A will be

Find the surface density of electric charge at a place on the earth's surface where the rate of fall of potential is 2.5 V

Two large plane parallel conducting plates are situated $40\mathrm{ }\mathrm{m}\mathrm{m}$ apart, as shown in the figure. The potential difference between the plates is $V$. What is the potential difference between point $X$ and point $Y$?

A uniform electric field of magnitude $5\times {10}^3\mathrm{ }\mathrm{N} {\mathrm{C}}^{-1}$ is directed along with the negative $x$-direction. Coordinates of point $A$ in the figure are $\left(–40\mathrm{ }\mathrm{c}\mathrm{m}, +20\mathrm{ }\mathrm{c}\mathrm{m}\right)$ and those of point $B$ are $\left(20\mathrm{ }\mathrm{c}\mathrm{m},\mathrm{ }-60\mathrm{ }\mathrm{c}\mathrm{m}\right)$. The potential difference between $A$ and $B$, i.e., $V_{\mathrm{A}}–V_{\mathrm{B}}$ along the arc of a circle of radius $2\mathrm{ }\mathrm{m}$ is

The potential of the electric field produced by a point charge at any point $\left(x,\mathrm{ }y,\mathrm{ }z\right)$ is given by $V=3x^2+5$, where $x$, $y$ and $z$ are in metres and $V$ is in volts. The intensity of the electric field at $\left(-2,\mathrm{ }1,\mathrm{ }0\right)$ is

The electric potential $\mathrm{V}$ is given as a function of distance $\mathrm{x}$ (meter) by $\mathrm{V}=\left(5{\mathrm{x}}^2+10\mathrm{x}-4\right) \mathrm{V}$. Value of electric field at $\mathrm{x}=1\mathrm{ }\mathrm{m}$ is

Two conducting charged spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ have the same surface potential. Then the ratio of electric fields near the surfaces is

Given, the electric potential at a point is, $\varphi =x^{2}y+yz$ . The electric field at the point $\left(1,\mathrm{ }3,\mathrm{ }1\right)$ is

When a charge of $3\mathrm{ }\mathrm{C}$ is placed in a uniform electric field, it experiences a force of $3\times {10}^3\mathrm{ }\mathrm{N}$ . Within this field, potential difference between two points separated by a distance of $0.01\mathrm{ }\mathrm{m}$ is

Figure shows the variation of electric field intensity with distance $\mathrm{x}$ . The potential difference between the points at $\mathrm{x}=2\mathrm{m}$ and $\mathrm{x}=6\mathrm{m}$ from the orgin 'O' is

A uniform electric field, having magnitude $E_0$ and direction along the positive $x$-axis, exists. If the potential $V$ is zero at $X=0$, then its value at $X=+x$ will be

The potential for a field is given by $V=x^2-y^2$. Electric field lines can be best represented by

If an electric field is $\overrightarrow{E}=10x\mathrm{ }\hat{\mathrm{i}}$ and considering the potential at $(10,\mathrm{ }20)$ to be zero, find the potential at the origin.

Figure shows the variation of electric field intensity with distance $\mathrm{x}$. What is the potential difference between the points at $\mathrm{x}\mathrm{ }=\mathrm{ }2\mathrm{m}$ and $\mathrm{x}\mathrm{ }=\mathrm{ }6\mathrm{m}$ from 0 ?

Determine the electric field, if the potential of this field depends on $x$, $y$ co-ordinates as $V=10\mathrm{ }axy$.