Physics Electric Charge and Field

Consider the force F on a charge ' q ' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if ' q ' is placed at distance r from the centre of the shell?

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale)

A charged particle (mass m and charge q) moves along x axis with velocity V₀. When it passes through the origin it enters a region having uniform electric field E = -Ej which extends upto x = d. Equation of path of electron in the region x > d is:

Charge Q? and Q? are at point A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q?/Q? is proportional to:

Two infinite planes each with uniform surface charge density $+\sigma$ $$ are kept in such a way that the angle between them is ${30}^{?}$ ${}^{}$ . The electric field in the region shown between them is given by:

A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be:

What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other?

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance 2 m when each is carrying same charge q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1m). The particle executes SHM. Its angular frequency of oscillation will be ______ * 10? rad/s if q' = 1 C.

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle 'θ' with the vertical?

An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field $200\frac{N}{C}$  as shown in the figure. A body of mass 1kg and charge 5 mC is allowed to slide down from rest at a height of 1m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

$\left[g=9.8m/s^2;sin30°=\frac{1}{2};cos30°=\frac{\sqrt[]{3}}{2}\right]$