ELECTROSTATIC POTENTIAL

Question 1

Two uniformly large parallel thin plates having charge densities are kept in the X-Z plane at a distance 'd' apart. Sketch an equipotential surface due to electric field between the plates. If a particle of mass m and charge '-q' remains stationary between the plates, what is the magnitude and direction of this field?

OR

Two small identical electrical dipoles AB and CD, each of dipole moment 'p' are kept at an angle of as shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field directed along + X direction, what will be the magnitude and direction of the torque acting on this?

Ans.

Here the red dotted lines represent the parallel equipotential surfaces along X-Z plane.

If a charge q has to be held stationary between the two plates, it will have to be balanced by two forces.

Gravitational force: mg, downwards

Electrostatic force= 2qE, acting upwards

This implies that in XZ plane, the upper plate is + charged plate and lower plate is –charged plate.

So, E field lines have to be directed along –y axis.

OR

Resultant dipole moment,

Direction of resultant dipole moment :

That is, 30 degrees with +x axis.

Given applied E is along +x axis,

So torque on resultant dipole will be

=pEsin30 =pE /2

Direction will be along -z axis.Question 2

A point charge Q is placed at point O as shown in the figure. Is the potential difference positive, negative or zero, if Q is (i) positive (ii) negative?

Ans.

Potential at a point : V = kq/r

For any Q,

Where rA <rB

So 1/ rA >1/ rB

So, >0

If Q at O is Positive, VA-VB will be positive

If Q at O is Positive, VA-VB will be negative.

Question 3

Ans.

  Question 4

The two graphs drawn below, show the variations of electrostatic potential (V) with 1/r (r being the distance of field point from the point charge) for two point charges q1 and q2.

(i) What are the signs of the two charges.

(ii) Which of the two charges has the larger magnitude and why ?

Ans.

(i) The potential due to positive charge is positive and due to negative charge, it is negative, so, q1  is negative and  q2 is positive.

(ii) 

As the magnitude of slope of the line due to charge q2 is greater than that due to q1, q2 has larger magnitude

  Question 5what is what?Ans.   Question 6Consider a region where electric field is zero, Is it necessary that electric potential is also zero where electric field strength is zero? Give any two examples to illustrate your answer.Ans. We know that the electric field is equal to the

negative of potential gradient . This implies that even if the electric field at a point is zero, the potential may have some non-zero constant value at that point. (1) Electric field inside a charged conducting sphere is zero but potential at any point inside is the same as that on the surface of the sphere. (2) Electric field at mid point of line joining two equal and similar charges is zero, but the potential at this point is twice of that due to a single charge.

  Question 7Two positive point charges of 0.2 C and 0.01 C are placed 10 cm apart. Calculate the work done in reducing the distance to 5 cm.Ans.

Work done in reducing the distance from 10 cm to 5 cm can be calculate by using the

relation W =    

  Question 8Calculate the electric potential at a point X due to a charge 1 C located at 10 cm from it. Also calculate the work done in bringing a charge of 2  10-9 C from infinity to the point X.Ans.

Electric potential at a point X due to the point charge of 1 C located at 10 cm from it is

.

The work done in bringing a charge of 2  10-9 C from infinity to the point X is given by:W = qo VW = 2  10-9 C 9  104 V = 18  10 -5 J = 1.8 x 10-4 J  Question 9Points A, B, and C are situated at the circumference of a circle of radius r and a charge q is placed at its centre. A charge qo is brought from external point P away from the circle to A, B, C. In which case work done is maximum?Ans.

Potential at the points A, B, and C will be same as they lie on circumference of the circle. Hence the work done in bringing the charge qo from point P to any of the points A, B, and C will exactly same.

  Question 10When a point charge is moved closer to a similar charge of greater magnitude, its potential increases or decreases?Ans.

When a point charge is moved closer to a similar charge, work has to be done against

the repulsive force. This work is stored as potential energy and hence increases the potential of the charge.

Question 11The electric potential at a point 0.9 m from a point charge is + 50 V. What is the magnitude and sign of the charge?Ans.

The polarity of the charge is positive.  Question 12What would be the work done if a point charge +q, is taken from a point P to the point Q on the circumference of a circle drawn with another point charge +q at the centre?Ans.

Work done is zero, because on the circumference, distance between two charges remains the same. Hence, VA = VB.

  Question 13

Two point A and B at a distance of 10 cm are each at a potential of 10 V. What will be the work done to move a positive charge of 1 C from A to B?Ans.

Zero, because both the points are at same potential.

 Question 1410 J of work is done in moving a positive charge of 1 C between two points. What is the potential difference between these two points? Ans.

Potential difference = Work/charge = 10 J/ 1C = 10 V.

Question 15What do you mean by potential difference of 1 volt?Ans.

The potential difference between two points is said to be 1 volt if 1 joule of work is done in moving a positive charge of 1 coulomb from one point to the other against the electrostatic force.