When a charged comb is brought near a small piece of paper, it attracts the piece. Does the paper become charged when the comb is brought near it?

Total charge –Q is uniformly spread along length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring.

(a) Show that the particle executes a simple harmonic oscillation.

(b) Obtain its time period.

Five charges, q each are placed at the corners of a regular pentagon of side ‘a’ (Fig. 1.12).

(a) (i) What will be the electric field at O, the center of the pentagon?

(ii) What will be the electric field at O if the charge from one of the corners (say A) is removed?

(iii) What will be the electric field at O if the charge q at A is replaced by –q?

(b) How would your answer to (a) be affected if pentagon is replaced by n-sided regular polygon with charge q at each of its corners?

Fig. 1.10 represents a crystal unit of cesium chloride, CsCl. The cesium atoms, represented by open circles are situated at the corners of a cube of side 0.40nm, whereas a Cl atom is situated at the centre of the cube. The Cs atoms are deficient in one electron while the Cl atom carries an excess electron.

(i) What is the net electric field on the Cl atom due to eight Cs atoms?

(ii) Suppose that the Cs atom at the corner A is missing. What is the net force now on the Cl atom due to seven remaining Cs atoms?

The electric force experienced by a charge of 1.0 × 10^–6 C is 1.5 × 10^–3 N. Find the magnitude of the electric field at the position of the charge.

A point charge produces an electric field of magnitude 5 N C^–1 at a distance of 40 cm from it. What is the magnitude of the charge?

A particle of mass 1g and charge 2.5 × 10^–4 C is released from rest in an electric field of 1.2 × 10⁴ N C^–1.

(a) Find the electric force and the force of gravity acing on this particle. Can one of these forces be neglected in comparison with the other for approximate analysis?

(b) How long will it take for the particle to travel a distance of 40 cm?

(c) What will be the speed of the particle after travelling this distance?

(d) How much is the work done by the electric force on the particle during this period?

The bob of a simple pendulum as a mass of 40g and a positive charge of 4.0 × 10^–6 C. It makes 20 oscillations in 45s. A vertical electric field pointing upward and the magnitude 2.5 × 10⁴ N C^–1 is switched on. How much time will it now take to complete 20 oscillations?

Consider the situation of figure. The work done in taking a point charge from P to A is W_A, from P to B is W_B and from P to C is W_C.