Electric Charges and Fields Class 12 Important Questions

Electric Charges and Fields Class 12 Important Questions

Electric Charges and Fields is the first chapter of Class 12 Physics. It explains what electric charge is, how charges attract and repel each other (Coulomb's law), how an electric field is drawn and measured, how an electric dipole behaves in a field, and how Gauss's law is used to find the field of a charged sheet, wire or sphere. These ideas are the base for the whole electrostatics unit, and the board exam asks numericals and short derivations from this chapter every year.

On this page, Extramarks experts have put together 12 important questions from Electric Charges and Fields with step-by-step answers. The set covers field-line diagrams, dipole numericals, charges at the corners of a square, forces on a charge at the centre of a hexagon, Coulomb's law in vector form and Gauss's law applications. Solve each question yourself first, then check your working against the answer given below it.

Physics Class 12 Chapter 1 Important Questions

Electric Charges and Fields
Medium
Q.
What is the force between two small charged spheres having charges of 2 × 10−7 C and 3 × 10−7 C placed 30 cm apart in air?
Electric Charges and Fields
Medium
Q.
The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge − 0.8 μC in air is 0.2 N.
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?
Electric Charges and Fields
Medium
Q.
Check that the ratio ke2/Gmemp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
Electric Charges and Fields
Easy
Q.
(a) Explain the meaning of the statement ‘electric charge of a body is quantised’.
(b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?
Electric Charges and Fields
Medium
Q.
When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
Electric Charges and Fields
Medium
Q.
Four point charges qA = 2 μC, qB = −5 μC, qC = 2 μC, and qD = −5 μC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 μC placed at the centre of the square?
Electric Charges and Fields
Medium
Q.
(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
(b) Explain why two field lines never cross each other at any point?
Electric Charges and Fields
Medium
Q.
Two point charges qA = 3 μC and qB = −3 μC are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges?
(b) If a negative test charge of magnitude 1.5 ×  10−9 C is placed at this point, what is the force experienced by the test charge? 
Electric Charges and Fields
Medium
Q.
A system has two charges qA = 2.5 × 10−7 C and qB = −2.5 × 10−7 C located at points A: (0, 0, − 15 cm) and B: (0, 0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
Electric Charges and Fields
Medium
Q.
An electric dipole with dipole moment 4 × 10−9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 N C−1. Calculate the magnitude of the torque acting on the dipole.
Electric Charges and Fields
Medium
Q.
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10−7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
Electric Charges and Fields
Medium
Q.
(a) Two insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10−7 C? The radii of A and B are negligible compared to the distance of separation.
(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
Electric Charges and Fields
Medium
Q.
Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?
Electric Charges and Fields
Easy
Q.
Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field.
Give the signs of the three charges. Which particle has the highest charge to mass ratio?
Electric Charges and Fields
Medium
Q.
Consider a uniform electric field E = 3×10 3 i ^    NC -1 .  (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?  (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?
Electric Charges and Fields
Medium
Q.
What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?
Electric Charges and Fields
Medium
Q.
Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 × 103 N m2C-1.
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?
Electric Charges and Fields
Easy
Q.
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
Electric Charges and Fields
Medium
Q.
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
Electric Charges and Fields
Medium
Q.
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 NC-1 and points radially inward, what is the net charge on the sphere?
Electric Charges and Fields
Medium
Q.
A point charge causes an electric flux of −1.0 × 103 Nm2C-1 to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge.
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
(b) What is the value of the point charge?
Electric Charges and Fields
Medium
Q.
A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0  μCm-2.
(a) Find the charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?
Electric Charges and Fields
Medium
Q.
An infinite line charge produces a field of 9 × 104 NC-1 at a distance of 2 cm. Calculate the linear charge density.
Electric Charges and Fields
Medium
Q.
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0×10-22 Cm-2. What is E→:  (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?     
Electric Charges and Fields
Medium
Q.
An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 NC−1 in Millikan’s oil drop experiment. The density of the oil is 1.26 gcm−3. Estimate the radius of the drop. (g = 9.81 ms−2; e = 1.60 × 10−19 C).
Electric Charges and Fields
Medium
Q.
Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?
Electric Charges and Fields
Difficult
Q.
In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC−1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10−7 C-m in the negative z-direction?
Electric Charges and Fields
Medium
Q.
(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.
(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig.1.36(b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
Electric Charges and Fields
Easy
Q.
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is, where is the unit vector in the outward normal direction, and is the surface charge density near the hole.
Electric Charges and Fields
Difficult
Q.
Obtain the formula for the electric field due to a long thin wire of uniform linear charge density λ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]
Electric Charges and Fields
Medium
Q.
It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge (+2/3) e, and the ‘down’ quark (denoted by d) of charge (−1/3) e,  together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.
Electric Charges and Fields
Difficult
Q.
(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.
Electric Charges and Fields
Easy
Q.
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 qEL2/ (2m vx2).
Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.
Electric Charges and Fields
Medium
Q.
Suppose that the particle in Exercise in 1.33 is an electron projected with velocity vx= 2.0 × 106 m s−1. If E between the plates separated by 0.5 cm is 9.1 × 102 NC-1, where will the electron strike the upper plate? (| e | =1.6 × 10−19 C, me = 9.1 × 10−31 kg.)

Q1. Draw the electric field lines for an electric dipole consisting of charges +q and -q separated by distance '2a'. Explain why:

Physics Class 12 Chapter 1 Important Questions

(i) The number of electric field lines originating from the positive charge equals the number terminating at the negative charge in the electric dipole; and (ii) the net flux through a Gaussian surface having the dipole at its center is zero

Answer: Electric Field Lines of a dipole

Class 12 Physics Ch 1 Q1 ans

(i) Since the number of field lines originating from a charge is proportional to the magnitude of the charge, and both charges have equal magnitudes, the number of field lines should be the same for both charges.

(ii) Since the net charge inside the Gaussian surface is zero, using Gauss's law (∮ E ⋅ dA = q / ε₀), we can conclude that the flux is zero.

Q2. With the help of a diagram, explain the path of a negatively charged particle projected at velocity v parallel to two charged plates (one positive, one negative) as shown. Assume a uniform electric field E perpendicular to the velocity, with charge q in gravity-free space.

Class 12 Physics Ch 1 Q2

Answer:

Class 12 Physics Ch 1 Q2 ans

Motion in x-direction

Class 12 Physics Ch 1 Q2 ans

x = vt (∵ ax = 0)

Motion in y-direction

Class 12 Physics Ch 1 Q2 ans

Hence, parabolic path of charge particle

Q3. A short electric dipole consists of charges +8μC and -8μC separated by 4 cm. The dipole is placed in a uniform external electric field of 2 × 10⁵ N/C making an angle of 60° with the dipole axis.

(a) Calculate the electric field intensity due to dipole at a point P located 15 cm from the center of the dipole along the perpendicular bisector of the dipole axis

(b) Determine the net torque acting on the dipole

Answer: (a): Electric Field at Point P due to dipole

Dipole moment: p = q × 2a = 8 × 10⁻⁶ × 0.04 = 3.2 × 10⁻⁷ C·m

Distance from center: r = 0.15 m

For point on the perpendicular bisector of dipole,

E = (1/4πε₀) × (p/r³)

Substitute values and calculate

E = (9 × 10⁹) × (3.2 × 10⁻⁷)/(0.15)³

E = (9 × 10⁹) × (3.2 × 10⁻⁷)/(3.375 × 10⁻³)

E = 8.53× (10^5) N/C

(b): Torque on Dipole

τ = p × Eext × sin θ

τ = (3.2 × 10⁻⁷) × (2 × 10⁵) × sin(60°)

τ = (3.2 × 10⁻⁷) × (2 × 10⁵) × (√3/2)

τ = 5.54 × 10⁻² N·m

Q4. Figure shows a neutral metallic sphere with a point charge+ Q placed near its surface. Electrostatic equilibrium conditions exist on metallic sphere.

Class 12 Physics Ch 1 Q4

Is the net flux through the right half of the Gaussian surface negative, positive, or zero? Also, what is the net flux through the Gaussian surface due to the charges appearing on the outer surface of the metallic sphere? Explain your answer.

Answer: Due to negative induced charges on the right side of sphere, the net flux through right half of Gaussian surface is negative

Since total induced charge inside the Gaussian surface is zero, the net flux is also zero

Q5. A square ABCD of side 12 cm has four identical point charges each of magnitude, +4μC, placed at its corners.

(a) Calculate the magnitude and direction of the net electric field at the center of the square

(b) Draw the diagram of electric field direction if one of the charges is missing

Answer: (a) Each point charge will cancel the electric field acting due to another charge placed diagonally as shown.

Class 12 Physics Ch 1 Q5 ans

Class 12 Physics Ch 1 Q5 ans

(b)

Class 12 Physics Ch 1 Q5 ans

As electric field due to q2 and q4 cancel each other, field due to q1 will only be present. Hence, the direction is towards B.

Q6. Two fixed point charges +8 μC and +18 μC are placed at points A and B respectively, separated by a distance of 20 cm in air. Find

(a) the point in between charges +8 μC and +18 μC where electric field is zero.

(b) Force acting on the third charge, +10 μC, when placed at the position as mentioned in (a)

(c) If the third charge is displaced towards +8 μC, will it return to its original position again?

Answer: (a): Net electric field due to both charges must cancel each other. Consider this point is at x distance from +8 μC. Hence k(8)/x² = k(18)/(20 – x)²

2/x = 3/(20 – x)

⇒x = 8 cm

(b): As net electric field at 8 cm from + 8 μC is zero and since F = q E, the force acting on the third charge, +10 μC, will also be zero.

(c): Yes, it will return to the same position as net electric field will be away from +8 μC.

Q7. A student rubs a glass rod with a piece of silk cloth. Initially, both are electrically neutral. After rubbing, the glass rod acquires a charge of

Class 12 Physics Ch 1 Q7

Class 12 Physics Ch 1 Q7

(a)What charge is acquired by the silk cloth?

(b)Name the law illustrated in this process.

(c)Calculate the number of electrons transferred.

Class 12 Physics Ch 1 Q7

Answer:

Class 12 Physics Ch 1 Q7 ans

So, 2000 electrons are transferred from the glass rod to the silk cloth.

Q8. Mention some basic properties of electric charges.

Answer: Some basic properties of electric charges are: 1. Like charges repel each other where as unlike charges attract each other. 2. If a system contains n charges i.e. q1, q2 - - - qn ,then, total charge on the system is q1 + q2 + q3 + - - - + qn. 3. The total charge of the isolated system is always conserved. 4. All free charges are integral multiple of a basic unit of charge i.e. (Charge q on a body is q = ne) also called quantization of charge. 5. The charge of a body refers only to its excess charge.

Q9.

Class 12 Physics Ch 1 Q9

Answer: Consider a regular hexagon with centre at origin.

Class 12 Physics Ch 1 Q9 ans

Class 12 Physics Ch 1 Q9 ans

For a regular hexagon, all vertices are at distance 'a' from centre. The vertices make angles 0°, 60°, 120°, 180°, 240°, 300° with positive x-axis.

Class 12 Physics Ch 1 Q9 ans

Net force is given by

Class 12 Physics Ch 1 Q9 ans

The net force is zero due to symmetry.

Q10. Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10⁻²² C/m². What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

Answer:

Class 12 Physics Ch 1 Q10 ans

The situation of the problem is represented in the given figure.

Here, A and B are two parallel plates close to each other. Outer region of plate A is labeled as I, the region between the plates, A and B, is labelled as II and outer region of plate B is labelled as III.

Class 12 Physics Ch 1 Q10 ans

Class 12 Physics Ch 1 Q10 ans

Q11.

Class 12 Physics Ch 1 Q11

on the conducting sphere.

Answer:

Class 12 Physics Ch 1 Q11 ans

inside the conductor. To conserve charge, a total charge of will be distributed on the outer surface of the sphere. Thus, the charge on the outer surface will be:

Q+q

Class 12 Physics Ch 1 Q11 ans

Therefore, the charge distribution is: Inner surface of the cavity: -q Outer surface of the sphere: Q+q

Q12.

Class 12 Physics Ch 1 Q12

Answer: Coulomb's Law in Vector Form:

Class 12 Physics Ch 1 Q12 ans

On finding position vector we have,

Class 12 Physics Ch 1 Q12 ans

Now we calculate force,

Class 12 Physics Ch 1 Q12 ans

Class 12 Physics Ch 1 Q12 ans

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FAQs (Frequently Asked Questions)

The most important numericals are based on Coulomb’s law, electric field at a point, electric dipole moment, torque on a dipole, electric flux, and Gauss’s law. These are common 2-mark, 3-mark, and 5-mark question areas.

Chapter 1 physics class 12 important numerical questions usually include one Coulomb’s law problem, one flux or Gauss’s law problem, and one dipole-based question. Derivations from dipole field and Gauss’s law applications are also important.

Convert all charges into coulombs and distance into metres. Then use F = kq₁q₂/r². After finding magnitude, check signs of charges to decide whether the force is attractive or repulsive.

Gauss’s law connects electric flux with enclosed charge. It is used to derive electric field due to an infinite wire, infinite sheet, and spherical shell. These derivations often appear as 5-mark questions in board-style exams.

The most important derivations are electric field on the axial line of a dipole, torque on a dipole in a uniform electric field, Gauss’s law, field due to infinite wire, field due to infinite sheet, and field inside and outside a spherical shell.

Avoid using cm instead of m, μC instead of C, and scalar addition instead of vector addition. Also check field direction, charge signs, flux angle, and whether the Gaussian surface actually encloses charge.