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AL-LQ-Electrostatics / p.1
1.
(95-I-2)
In the figure, a potential difference is applied across two parallel plates to establish a region of uniform
electric field in between. An electron is fired with an initial velocity of 3  10 ms
6
After 5  10
8
1
s, the electron leaves the parallel plates with a velocity of 5  10 ms
6
into that region.
1
.
Assume that the electric field is zero outside the region in between the parallel plates. The effect of
gravity on the electron is negligible.
(Given : mass of electron =
(a)
9  10 31 kg .)
What is the direction of the force acting on the electron when it is between the parallel plates?
(1 mark)
(b)
Sketch on the above figure the path of the electron, showing its flight both inside and outside the
region between the parallel plates.
(c)
(2 marks)
Find the change in electric potential energy of the electron after flying between the parallel plates.
(2 marks)
(d)
Find the magnitude of the acceleration of the electron when it is between the parallel plates.
(3 marks)
(e)
Find the displacements of the electron in x- and y- direction after flying between the parallel
plates.
(f)
What would the time of flight and the displacement in y-direction of the electron be if the
potential difference across the plates is doubled? Explain briefly.
2.
(2 marks)
(98-I-4)
(4 marks)
AL-LQ-Electrostatics / p.2
A sheet of carbon paper of uniform conductivity has been painted with two parallel, rectangular silver
strips as shown below. Points
Ao and Bo on the two strips are connected to a battery of e.m.f. 6 V.
The negative terminal of an ideal voltmeter is connected to
(a)
Ao and its positive terminal is a probe P.
What is the voltmeter reading when P is connected to B0? What would be observed when P is
moved along B1B2?
(b)
(2 marks)
Now the probe is moved along A0 B0 and the voltage reading V recorded is plotted against the
distance x of the probe from A0
(i)
Explain the variation of V along
Ao Bo .
(ii)
Find the electric field strength at point X. State its direction.
(2 marks)
(3 marks)
(iii) Neglecting edge effect, sketch on the above figure the equipotential lines at 1 V intervals
between the two silver strips.
(c)
(2 marks)
An additional silver strip is now painted in between the two strips present as shown below.
(i)
Sketch on the graph in (b) the variation of voltage V with distance x of the probe from Ao .
(2 marks)
(ii)
State and explain the change, if any, in the electric field strength at point X.
(2 marks)
AL-LQ-Electrostatics / p.3
3.
(02-IA-3)
A metal sphere has its center fixed at O as shown in Figure 3.1. The radius of the sphere is r 0 and it carries a
negative charge –Q. The electric potential at infinity is taken to be zero.
12
1
2
(Given: permittivity of free space = 8.85  10 C N m )
(a) (i)
Write an expression for the electric potential V0 on the surface of the sphere.
2
(ii)
If Q  2.2  1011C and V0  10V , find ro.
(iii)
Let B be a point at a distance rB from O. Sketch the variation of the potential VB at B for all values of
rB.
(b)
(i)
A particle of small positive charge q is held stationary by an external force at B where r B = 5 cm.
Find the magnitude of the force required in terms of q and state its direction.
(ii)
If the particle at B is projected with speed v such that it can escape from the electric field of the
sphere, find the minimum value of v. The charge-to-mass ratio of the particle is 1.76  1011Ckg1 .
(Hint: Consider the energy possessed by the particle.)
AL-LQ-Electrostatics / p.4
4.
(03-IIB-6)
A ball with a conducting paint surface is connected to the positive terminal of an E.H.T. It is suspended 0.5 m
above the bench and away from the walls using a nylon thread. A flame probe consisting of a hypodermic needle
is connected to a calibrated electroscope to record the electric potentials at the points in space around the ball. The
flame probe is placed close to, but not touching, the ball at the same level as the ball’s center as shown in Figure
6.1.
(a)
Draw lines on the figure to show how the pieces of apparatus are connected by wires according to the above
description, and in doing so ensure that the experiment can be performed safely.
(b)
(3 marks)
Explain why a voltmeter or a CRO cannot be used to measure the electric potential in this experiment.
(1 mark)
(c)
Explain why a small gas flame is required to be lit at the tip of the hypodermic needle.
(2 marks)
(d)
The flame probe is moved horizontally around the ball at a fixed distance from the center of the ball.
Describe the change, if any, in the reading of the electric potential from the electroscope. Explain briefly.
(2 marks)
(e)
The flame probe is gradually moved away from the ball, keeping it at the same level as the centre of the ball.
Readings of the distance of the probe from the ball’s centre and the electric potential indicated by the
electroscope are tabulated as follows:
Distance from centre
of ball r/cm
10
11
12
15
17.5
20
Electric potential V/V
1000
900
800
600
500
400
1
/cm-1
r
(i)
Plot a graph of V against
1
. (3 marks)
r
AL-LQ-Electrostatics / p.5
(ii) Explain why the graph does not pass through the origin.
(2 marks)
(iii) If a small quantity of positive charge q is moved with uniform velocity from a point 11 cm from the
ball’s centre to another 10 cm from its centre, what is the work done on it in terms of q? Estimate the
average electric field strength E between these two points.
(2 marks)