Q. 334.3( 17 Votes )
A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx(like particle 1 in Fig. 1.33). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is
Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.
Mass of the particle = m
Charge of the particle = -q
Velocity of the particle = vx
Length of the plate = L
Electric field between the plates = E
From Newton’s second law of motion,
Where, F = Force on the particle
m = mass of the particle
a = acceleration of the particle
⇒ (Since F = qE)
Time taken by the particle to cover the distance L is given by
(Time = Displacement/Velocity)
For the movement in vertical direction, initial velocity (u) is zero.
According to Newton’s second equation of motion,
This is the vertical displacement of the particle at the far edge of the plate.
This motion is very similar to the motion of a projectile in a gravitational field. In a gravitational field, the force acting on the particle is mg and in the given case it is qE. The trajectory followed by the object will be similar in both the cases.
NOTE: A projectile is any object thrown into space by the exertion of a force. The path followed by a projectile is known as its trajectory.
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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?
Physics - Exemplar
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?
Physics - Exemplar
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 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?
HC Verma - Concepts of Physics Part 2
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?
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A rod of length L has a total charge Q distribute uniformly along its length. It is bent in the shape of a semicircle. Find the magnitude of the electric field at the centre of curvature of the semicircle.
Consider a uniformly charged ring of radius R. Find the point on the axis where the electric filed is maximum.