Electric potential

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to ∞) on its surface. For this sphere the equipotential surfaces with potentials $\dfrac{3V_0}2$, $\dfrac{5V_0}4$, $\dfrac{3V_0}4$ and $\dfrac{V_0}4$ have radius $R_1$, $R_2$, $R_3$ and $R_4$ respectively. Then

An electric field $\vec E=\left(25\hat i+30\hat j\right)$ NC$^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x=2$ m, $y=2$ m is :

Assume that an electric field $\vec E=30x^2\,\hat i$ exists in space. Then the potential difference $V_A-V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x=2$ m is :

Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec E(r)|$ and the electric potential $V(r)$ with the distance $r$ from the centre, is best represented by which graph?

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K=\dfrac1{4\pi\varepsilon_0}\dfrac q{L^2}$, which of the following statement(s) is(are) correct?

A spherical metal shell A of radius $R_A$ and a solid metal sphere B of radius $R_B$ ($<R_A$) are kept far apart and each is given charge '$+Q$'. Now they are connected by a thin metal wire. Then

Which of the following statement(s) is/are correct?

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A\times10^{Z}$ (where $1<A<10$). The value of '$Z$' is

Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let $E$ be the electric field and $V$ be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let $B$ be the magnetic field at M and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

Consider a system of three charges $\frac q3$, $\frac q3$ and $-\frac{2q}3$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius $R$ and angle CAB = 60°.

STATEMENT-1: For practical purposes, the earth is used as a reference at zero potential in electrical circuits.

and

STATEMENT-2: The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\dfrac{Q}{4\pi\varepsilon_0R}$.

Positive and negative point charges of equal magnitude are kept at $\left(0,0,\frac a2\right)$ and $\left(0,0,\frac{-a}2\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a,0,0)$ to $(0,a,0)$ is