The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

The electric field is in the direction of the $x$-axis. The work done to move a charge of $0.2 \ C$ by a distance of $2 \ m$ at an angle of $60^\circ$ with the $x$-axis is $4 \ J$. What is the value of the electric field $E$ in $N/C$?

$A$ uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

Two metal plates $(A, B)$ are kept horizontally with a separation of $(\frac{12}{\pi}) \text{ cm}$, with plate $A$ on the top. An atomizer jet sprays oil (density $1.5 \text{ g/cm}^3$) droplets of radius $1 \text{ mm}$ horizontally. All oil droplets carry a charge of $5 \text{ nC}$. The potentials $V_A$ and $V_B$ are required on plates $A$ and $B$ respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are . . . . . . . (Neglect the air resistance to the droplets and take $g = 10 \text{ m/s}^2$)

The diagram shows three infinitely long uniform line charges placed on the $X, Y$ and $Z$ axes with linear charge densities $2\lambda, 3\lambda$ and $\lambda$ respectively. The work done by an external agent in moving a unit positive charge from $(1, 1, 1)$ to $(0, 1, 1)$ is equal to:

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is: