Electrostatics MCQ On Pre Entry Test 3

1. Two equal charges + q are placed at points A and B. A small charge –q0 at the midpoint C joining A and B. If –q0 is slightly displaced along a straight line perpendicular to AB and release it will:

(a) remain stationary in the displaced position

(b) come back to C

(c) continue to move away from C

(d) oscillate about C

2. 27 identical drops of mercury , charged to same potential of 10V are made to combine to form one large drop. The potential of the large drop will be:

(a) 45V

(b) 90 V

(c) 135 V

(d) 270 V

3. An infinite number of electric charges each equal to Q are placed on the x=axis at x = 1 , 2 , 4, 8,……….. metre. The potential at x = 0 will be :

(a) zero

(b) Q/6πε0

(c) Q/2πε0

(d) infinite

5. Charge Q is placed at the centre of a circle of radius R. charge q is at a distance r from Q. r < R. Charge q is moved alternately to two points one the circumference of the circle. The ration of the distance of these points from q is 1:2. The work done in first case W1 is related to the work done in the second case by :

(a) W1 > W2

(b) W1 = W2

(c) W1 < W2

(d) W1 = W2

6. A charge Q is placed at the centre of a cube. The electrical flux across a face of the square is :

(a) Q/4πε0

(b) Q/ε0

(c) Q/6ε0

(d) Q/4ε0

7. A parallel plate capacitor is charged by connecting is plates to he terminals of a battery. The battery remains connected and a glass plate in interposed between the plates of the capacitor, then:

(a) the charge on the plates will be reduced

(b) the p.d between the plates will be reduced

(c) the charge on the plates will increase

(d) the p.d. between the plates will increase

8. A parallel plate capacitor with plate area A and B separation d is filled with laminar strips of two dielectrics of permittivity’s ε1 and ε2 such that the volume occupied by each medium is the same. The capacitance of the capacitor is:

(a) 2 (ε1 + ε2) A/d

(b) 2 ε1 + ε2 A/d (ε1 + ε2)

(c) 2 (ε1 + ε2) A/d ε1 + ε2

(d) (ε1 + ε2) A/d .

9. Two capacitors C1 and C2 are connected in parallel and a total charge Q is given to the combination the ratio of the charge C1 to that C2 is :

(a) C1/C2

(b) C1 C2

(c) C2/C1

(d) 1/C1C2

10. Two insulated charged spheres of radii 0.2 m and 0.25 m respectively each carry the same charge + q. If connected by a thin copper wire and then separated :

(a) both spheres will have same charge + q

(b) charge on the smaller sphere will be more than that on the large one

(c) charge on the smaller sphere will be less than that on the larger one

(d) charge on each sphere will be +2q

Answer Keys:

1. (d) 2. (b) 3. (c) 4. (b)  5. (b) 6. (c) 7. (c) 8. (b) 9. (c) 10. (c)

Electrostatics MCQs On Pre Entry Test 2

1. A parallel plate condenser has a capacity of 10 μf. The distance between the plates in doubled without altering any other thing, the capacity (in μF) is now:

(a) 0.2

(b) 0.5

(c) 5

(d) 20

2. Three identical capacitors of capacity C, each are connected in series and this combination is connected in parallel with an identical condenser. The equivalent capacity of the whole combination is :

(a) 3C/4

(b) 4C/3

(c) 2C

(d) 3C

3. Three condensers of capacity C each, are connected as shows below in the figure :

The capacity of the combination between the points A and B is :

(a) 3C

(b) 3C/2

(c) 2C/3

(d) C/3

4. In a region where electric field is zero, the potential at a point.

(a) is zero every where

(b) is constant every where but not necessarily zero

(c) cannot be defined

(d) depends on the position of the point

5. The false statement for a dielectric medium is:

(a) If charge can be easily induced in the medium the dielectric constant is large

(b) The electric field within the medium in reduced due to induced charged on the surface

(c) The dielectric constant of the medium is small if it is metallic

(d) If it is vacuum, the value of dielectric constant is one

6. Two small charged balls are suspended from a common point of suspension by threads of equal length and negligible mass. Upon repulsion the threads make equal angles with the vertical. We may conclude that:

(a) masses of the balls are equal

(b) charges on the balls are equal

(c) both charges and the masses are equal

(d) neither the charges nor the masses are equal

7. Charges q1 and q2 are stationed at the centers of two identical cubes of side a meters an build up of a material of dielectric constant 4. If the centers of the cubes are held 2a apart with faces parallel each other the force of attraction repulsion between the charges is F. If the charges were instead held at a distance 2a apart in vacuum air the force of attraction repulsion between q1 and q2 is :

(a) 4F/9

(b) F/4

(c) 4F

(d) 9F/4

8. A conducting sphere A carries a charge + q. It is placed inside another conducting spherical shell B carrying charge Q. If A and B are connected by a wire:

(a) charge will flow from A to B

(b) Charge will flow from B to A

(c) charge will flow depending on the magnitude and sign of Q

(d) there will be no flow of charge

9. If the plates of charged parallel plate capacitor are brought closer together using insulated handles to move them.

(a) the charge on the plates increases

(b) the p.d across plates increase

(c) the p.d across plates decrease

(d) the p.d. across plates remains the same

10. Two point charges of + 10nC each are placed 1m apart in air. Then at the middle point of the line joining them:

(a) the field E = 0 and potential V=O[]

(b) E = 0 and V = 360 volts

(c) E = 720 N/C and V=0

(d) E=0 and V = –360 volts

Answer Keys:

1. (c) 2. (b)  3. (c) 4. (b) 5. (c) 6. (a) 7. (d) 8. (a)  9. (c) 10. (b)

Electrostatics Complete Theory Simple Way

ELECTROSTATICS

Electrical charge – It is the quantity of electricity contained in or on a body .

Coulomb – It is the unit of electric charge in the S.I. system .

The charge on one electron = 1.602 x 10–19 Coulomb

Coulomb’s Law – The force of attraction or repulsion between two charged bodies whose charges behave as through concentrated at a point is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them i.e.,

F = (in S.I. System)

Where,  = 9×109 Newton – metre2 coulomb2, ε0 = permittivity of free space and

K = relative permittivity of dielectric constant of the medium.

Here K is a dimensionless constant whose value is 1.005 for air, which is taken as unity for all practical purpose, thus for air the equation for F reduces to

F = 

Electric Field Intensity (E) – At any point it is defined as a vector whose magnitude and direction are equal to the force per unit charge on a very small charged body at that point.

Electric Potential (V) – It is defined as the amount of work done in taking a unit positive charge from infinity to the point of consideration.

Potential deference – The difference of potential between two points in an electric field is defined as the work done in taking a unit positive charge from one point to other against the electric force.

Electric field intensity (E) and potential (V) due to a point charge (q) at a distance ‘r’

E = Newton coulomb

V = Volt

Relation between E and V:

E = N/C

Where represents the potential gradient.

Electric field intensity (E ) and potential (V) due to an electric dipole – Two equal and opposite charges (+q& – q) separated by the distance 2/ form a dipole and its dipole moment (P) is directed from – q to + q along the line joining them

P = 2/ x q = 2q/

The electric field intensity (E) at a distance on it perpendicular bisector (r >> 2/) is

E = Newton / Coulomb

The electric field at a distance r on its axis (r >> 2/) is.

E = Newton / Coulomb

The electric potential at a distance ‘r’ on it’s perpendicular bisector is,

V = 0

The electric potential as at distance ‘r’ on it’s axis (r >> 2/) is,

V =  Volt

Capacitor – It is a device in which electric charge may temporarily be stored.

Capacity of a Capacitor (C) – If q is the charge given to a capacitor and V is the potential difference to which it has been raised, then,

C =  farad

Capacity of a sphere of radius ‘a’ metre –

C = 4πε0a farad

Capacity of a parallel plate Capacitor

C = farad in air

And C = farad in medium of dielectric constant K.

When ε0 = permittivity of free space (8.86 x 10–12 farad / metre)

A = area of one of the two plates

d = distance between the two plates

Electric Field between the plates of a parallel plate capacitor – A uniform electric filed is produced between the plates and its intensity is given by

E = 

Capacitor in series – For capacitors in series –

V = V1 + V2 + V3 + …….

Q = Q1 + Q2 = Q3 = ……..

Capacitors in parallel – For capacitors in parallel

V = V1 = V2 = V3 = ………………

Q = Q1 + Q2 + Q3 + ……………..

C = C1 + C2 + C3 + ………………

Energy of a charged capacitor –

E = 

Loss of energy in connecting two capacitors C1 and C2 charged to V1 and V2 –

Loss of energy = 

Capacitance of parallel plate capacitor when the space between the plates is partly filled with dielectric –

C =  farad

Where d = distance between the two plates of the capacitor

T = thickness of the dielectric

K = dielectric constant for the dielectric

Gauss’s Theorem – States that the total electric flux through a closed surface is equal to the ratio of the total electric charge Σq enclosed by the surface to the permittivity (s = ε0K) of the medium in which the charges are situated

Φ0 = 

Energy Density of Electric Field – equal ε0KE2

Remember:

1. Electric filed inside a charged conductor is zero.
2. Electric filed on and near a charged conductor is always normal to surface.

1. Surface of a conductor is an equipotential surface.
2. Charge density on a charged conductor is more at pointed surfaces than at flatter surface.
3. Density of electric lines of field force is a measure of E.
4. In charging a capacitor C to a voltage V through a resistor R the amount of energy spent by a source of emf is CV2 which is twice the energy stored in the capacitor.
5. A capacitor cannot by charged discharged instantly.
6. A capacitor hates a change in voltage across it and therefore REACTs.
7. A displacement current proportional to the rate of change of electric flux flows through a capacitor.
8. Coulomb force between two charges is extremely large compared to gravitational force of attraction between their masses.
9. A separation r between two charges kept in a dielectric medium of dielectric constant K is equivalent to a separation r  in vacuum / air.
10. A separation d between the plates of a parallel capacitor of area A filled with a dielectric is equivalent to a separation d/k if the space between plates were completely filled with vacuum /air.

Electrostatics MCQs For Pre Entry Test 1

1. Electric potential due to a point charge varies as :

(a) r

(b) r2

(c) 1/r

(d) 1/r2

2. Electrostatic potential is a:

(a) number

(b) vector

(c) tensor

(d) scalar

3. Electric intensity is a :

(a) scalar

(b) vector

(c) tensor

(d) number

4. Charges +2, – 4, + 8 and – 6 e.s.u. are placed at the four corner of a square of side 2 cm. The potential in e.s.u. at the centre of the square is:

(a) zero

(b) 20/ √2

(c) 16/ √2

(d) 12/ √2

5. Principal of superposition is applied to obtain the resultant of two or more forces due to point charges or linear surface space (volume) distribution of charges. Using this principal the magnitude of the resultant of three electrical forces 2F, F0 and F acting on a single charged particle, where F0 2F = 2F2 and F0 = 2FI , is

(a) F + F0

(b) [F2 + F02]1/2

(c) F √ 5

(d) F √ 7

6. The charge of the electron in coulombs is :

(a) + 4.8 x 10–10

(b) – 4.8 x 10–10

(c) + 1.6 x 10–10

(d) – 1.6 x 10–10

7. The electric filed intensity due to a point charge varies with the distance r from the charge as :

(a) 1/r

(2) 1/r2

(c) 1/r3

(d) 1/r4

8. A body carrying a net negative charge of coulomb has an excess of the flowing number of electrons:

(a) 9 x 102

(b) 3 x 1018

(c) 6.24 x 1018

(d) 1.602 x 1019

9. The total capacity of four equal condensers will be maximum when they are connected :

(a) all in series

(b) all in parallel

(c) partly in parallel and partly in series

(d) individually

10. Four condensers of capacities 4,6,8 and 16 microfarads are to be connected to a 1600 volts a.c. source. Each condensers can tolerate only 400 volts. This can be done without the damage in the circuit by connection:

(a) all condensers in series

(b) all condensers in parallel

(c) two in parallel and two in series

(d) three in parallel and one in series

Answer Keys:

1. (c) 2. (d) 3. (b) 4. (a) 5. (d) 6. (d)  7. (b) 8. (c) 9. (b) 10. (a)