JEE Physics Electric Charges And Fields MCQs Set 28

Physics Objective Questions and Answers: Electric Charges and Fields

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Multiple Choice Questions

Question 1: A point charge Q is placed in air and the net electric flux through a small area A is φ = E·A. On immersing the whole system in water (dielectric constant 80), the net electric flux through the same area
(a) becomes zero
(b) remains the same
(c) increases
(d) decreases
Show Answer & Explanation

Answer: (d) decreases

Explanation:
1. The field of the point charge is reduced by the dielectric constant K.
2. So the flux E·A through the same area decreases.

Teacher's Note:
1. E is divided by K.

Question 2: Match Column I with Column II.
Column IColumn II
(A) Additivity of charge(1) n + U-235 → Ba-144 + Kr-89 + 3n
(B) Conservation of charge(2) −5 μC + 15 μC = 10 μC
(C) Quantisation of charge(3) Gold nucleus repels an alpha particle
(D) Attraction and repulsion(4) q = ne

(a) A-2, B-4, C-1, D-3
(b) A-1, B-2, C-4, D-3
(c) A-2, B-1, C-4, D-3
(d) A-2, B-3, C-4, D-1
Show Answer & Explanation

Answer: (c) A-2, B-1, C-4, D-3

Explanation:
1. Charges add algebraically (A-2).
2. Total charge is the same before and after a nuclear fission (B-1).
3. Charge occurs in integral multiples of e (C-4).
4. Like charges repel, as a gold nucleus repels an alpha particle (D-3).

Teacher's Note:
1. Link the property with an example.

Question 3: Which of the following is the best insulator?
(a) carbon
(b) paper
(c) graphite
(d) ebonite
Show Answer & Explanation

Answer: (d) ebonite

Explanation:
1. Ebonite has a very high resistivity and holds charge well.
2. Carbon and graphite conduct, and paper is a poor insulator.

Teacher's Note:
1. Ebonite is an excellent insulator.

Question 4: A large non-conducting sheet carries a uniform charge density. Two uncharged metal rods A and B are placed near the sheet, side by side along a line perpendicular to the sheet. Then
(a) the sheet attracts A
(b) the sheet attracts B
(c) A attracts B
(d) all of the above
Show Answer & Explanation

Answer: (d) all of the above

Explanation:
1. The sheet's field polarises both rods by induction.
2. The induced opposite charges are nearer to the sheet, so it attracts both, and the induced dipoles A and B also attract each other.

Teacher's Note:
1. Induced charges always give attraction.

Question 5: The intensity of an electric field E due to a dipole depends on the distance r as
(a) \( E\propto\frac1r \)
(b) \( E\propto\frac1{r^2} \)
(c) \( E\propto\frac1{r^3} \)
(d) \( E\propto\frac1{r^4} \)
Show Answer & Explanation

Answer: (c) \( E\propto\frac1{r^3} \)

Explanation:
1. For a dipole at large distances E = kp/r³ (equatorial) or 2kp/r³ (axial).
2. So E ∝ 1/r³.

Teacher's Note:
1. Dipole field falls as 1/r³.

Question 6: An electric field can deflect
(a) neutrons
(b) X-rays
(c) γ-rays
(d) α-particles
Show Answer & Explanation

Answer: (d) α-particles

Explanation:
1. An electric field exerts a force only on charged particles.
2. α-particles are charged, whereas neutrons, X-rays and γ-rays are neutral.

Teacher's Note:
1. Only charged particles are deflected.

Question 7: The electric intensity due to a dipole of length 10 cm and having a charge of 500 μC, at a point on its axis at a distance of 20 cm from the nearer charge (the point lies outside the dipole), is
(a) \( 6.25\times10^{7}\ \text{N/C} \)
(b) \( 9.28\times10^{7}\ \text{N/C} \)
(c) \( 13.1\times10^{11}\ \text{N/C} \)
(d) \( 20.5\times10^{7}\ \text{N/C} \)
Show Answer & Explanation

Answer: (a) \( 6.25\times10^{7}\ \text{N/C} \)

Explanation:
1. The distances from the charges are 0.20 m and 0.30 m.
2. E = kq(1/0.2² − 1/0.3²) = 9 × 10⁹ × 5 × 10⁻⁴ × (25 − 11.1) = 6.25 × 10⁷ N/C.

Teacher's Note:
1. Subtract the two point-charge fields.

Question 8:
Assertion (A): On moving a distance two times the initial distance away from an infinitely long straight uniformly charged wire, the electric field reduces to one third of the initial value.
Reason (R): The electric field is inversely proportional to the distance from an infinitely long straight uniformly charged wire.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Starting at r and moving a further 2r puts the point at 3r.
2. Since E ∝ 1/r, the field becomes one third.

Teacher's Note:
1. E ∝ 1/r.

Question 9: If an object possesses an electric charge, it is said to be electrified or ____ A ____. When it has no charge, it is said to be ____ B ____. A and B refer to
(a) charged, neutral
(b) neutral, charged
(c) discharged, charged
(d) active, reactive
Show Answer & Explanation

Answer: (a) charged, neutral

Explanation:
1. A body with charge is a charged body.
2. A body without charge is neutral.

Teacher's Note:
1. Charged versus neutral.

Question 10: Electric flux over a surface in an electric field may be
(a) positive
(b) negative
(c) zero
(d) all of the above
Show Answer & Explanation

Answer: (d) all of the above

Explanation:
1. Flux = E·A can be positive, negative or zero depending on the angle between E and the area vector.

Teacher's Note:
1. Φ = EA cos θ.

Question 11: In the annihilation process, in which an electron and a positron transform into two gamma rays, which property of electric charge is displayed?
(a) additivity of charge
(b) quantisation of charge
(c) conservation of charge
(d) attraction and repulsion
Show Answer & Explanation

Answer: (c) conservation of charge

Explanation:
1. The total charge before the process (−e + e = 0) equals the charge after (0).
2. This shows conservation of charge.

Teacher's Note:
1. Net charge is conserved.

Question 12: A charged particle is free to move in an electric field. It will travel
(a) always along a line of force
(b) along a line of force, if its initial velocity is zero
(c) along a line of force, if it has some initial velocity in the direction of an acute angle with the line of force
(d) none of the above
Show Answer & Explanation

Answer: (d) none of the above

Explanation:
1. A particle starting from rest follows a line of force only if the line is straight.
2. In a non-uniform field with curved lines it does not, so none of the statements is always true.

Teacher's Note:
1. Lines of force may be curved.

Question 13:
Assertion (A): Some charge is put at the centre of a conducting sphere. It will move to the surface of the sphere.
Reason (R): A conducting sphere has no free electrons at the centre.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. Free charges on a conductor repel each other and move to the outer surface, so the assertion is true.
2. A conductor has free electrons everywhere, so the reason is false.

Teacher's Note:
1. Charge resides on the surface.

Question 14: At the centre of a cubical box a charge +Q is placed. The total flux coming out of one wall is
(a) \( Q/\varepsilon_0 \)
(b) \( Q/3\varepsilon_0 \)
(c) \( Q/4\varepsilon_0 \)
(d) \( Q/6\varepsilon_0 \)
Show Answer & Explanation

Answer: (d) \( Q/6\varepsilon_0 \)

Explanation:
1. The total flux Q/ε₀ divides equally among the 6 faces.
2. Each wall gets Q/6ε₀.

Teacher's Note:
1. Cube symmetry.

Question 15: A positively charged rod is brought near an uncharged conductor. When the rod is then suddenly withdrawn, the charge left on the conductor will be
(a) positive
(b) negative
(c) zero
(d) cannot say
Show Answer & Explanation

Answer: (c) zero

Explanation:
1. The conductor only gets polarised by induction and stays neutral overall.
2. On removing the rod the induced charges redistribute and the net charge is zero.

Teacher's Note:
1. Induction does not charge a body.

Question 16: An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that its axis makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole is zero when θ = 90°, the torque and the potential energy of the dipole will respectively be
(a) \( pE\sin\theta,\ -pE\cos\theta \)
(b) \( pE\sin\theta,\ -2pE\cos\theta \)
(c) \( pE\sin\theta,\ 2pE\cos\theta \)
(d) \( pE\cos\theta,\ -pE\sin\theta \)
Show Answer & Explanation

Answer: (a) \( pE\sin\theta,\ -pE\cos\theta \)

Explanation:
1. τ = pE sin θ.
2. With U = 0 at 90°, U = −pE cos θ.

Teacher's Note:
1. U = −p·E.

Question 17: If a body is negatively charged, then it has
(a) an excess of electrons
(b) an excess of protons
(c) a deficiency of electrons
(d) a deficiency of neutrons
Show Answer & Explanation

Answer: (a) an excess of electrons

Explanation:
1. Negative charge on a body means it has gained electrons.

Teacher's Note:
1. Negative means extra electrons.

Question 18:
Assertion (A): The force with which two charges attract or repel each other is not affected by the presence of a third charge.
Reason (R): The force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Coulomb forces obey the principle of superposition.
2. So each pair interaction is unaffected by other charges.

Teacher's Note:
1. Superposition of forces.

Question 19: If an electron has an initial velocity in a direction different from that of an electric field, the path of the electron is
(a) a straight line
(b) a circle
(c) an ellipse
(d) a parabola
Show Answer & Explanation

Answer: (d) a parabola

Explanation:
1. The electron has a constant acceleration along the field and a constant velocity component perpendicular to it.
2. This gives a parabolic path.

Teacher's Note:
1. Like projectile motion.

Question 20: Match Column I with Column II.
Column IColumn II
(A) Linear charge density(1) Charge/Volume
(B) Surface charge density(2) Charge/Length
(C) Volume charge density(3) Charge/Area
(D) Discrete charge distribution(4) System consisting of ultimate individual charges

(a) A-2, B-1, C-3, D-4
(b) A-2, B-3, C-4, D-1
(c) A-2, B-4, C-1, D-3
(d) A-2, B-3, C-1, D-4
Show Answer & Explanation

Answer: (d) A-2, B-3, C-1, D-4

Explanation:
1. λ = charge/length (A-2).
2. σ = charge/area (B-3).
3. ρ = charge/volume (C-1).
4. A discrete distribution is a system of individual charges (D-4).

Teacher's Note:
1. Definitions of densities.

Question 21: Gauss's law is true only if the force due to a charge varies as
(a) \( r^{-1} \)
(b) \( r^{-2} \)
(c) \( r^{-3} \)
(d) \( r^{-4} \)
Show Answer & Explanation

Answer: (b) \( r^{-2} \)

Explanation:
1. Gauss's law follows from the inverse square dependence of Coulomb's law.
2. Only for 1/r² does the flux through a sphere remain independent of its radius.

Teacher's Note:
1. Inverse square law.

Question 22: Select the correct statements. I. The electric field due to a charge outside the Gaussian surface contributes zero net flux through the surface. II. The total flux linked with a closed body not enclosing any charge will be zero. III. The total electric flux, if a dipole is enclosed by a surface, is zero.
(a) I and II
(b) II and III
(c) I and III
(d) I, II and III
Show Answer & Explanation

Answer: (d) I, II and III

Explanation:
1. Flux lines of an outside charge enter and leave, giving zero net flux (I and II).
2. A dipole has zero net charge, so its net flux is zero (III).

Teacher's Note:
1. Flux counts enclosed charge only.

Question 23: Gauss's law states that
(a) the total electric flux through a closed surface is 1/ε₀ times the total charge placed near the closed surface
(b) the total electric flux through a closed surface is 1/ε₀ times the total charge enclosed by the closed surface
(c) the total electric flux through an open surface is 1/ε₀ times the total charge placed near the open surface
(d) the line integral of the electric field around the boundary of an open surface is 1/ε₀ times the total charge placed near the open surface
Show Answer & Explanation

Answer: (b) the total electric flux through a closed surface is 1/ε₀ times the total charge enclosed by the closed surface

Explanation:
1. Gauss's law relates the flux through a closed surface to the charge inside it: Φ = q_enclosed/ε₀.

Teacher's Note:
1. Only enclosed charge counts.

Question 24: Two spheres A and B of exactly the same mass are given equal positive and negative charges respectively. Their masses after charging
(a) remain unaffected
(b) mass of A > mass of B
(c) mass of A < mass of B
(d) nothing can be said
Show Answer & Explanation

Answer: (c) mass of A < mass of B

Explanation:
1. A has lost electrons and B has gained the same number of electrons.
2. So the mass of A is slightly less than that of B.

Teacher's Note:
1. Electrons carry mass.

Question 25: An electric dipole has charges of magnitude q and dipole moment p. It is placed in a uniform electric field E with its moment along the direction of the field. The force on it and its potential energy are respectively
(a) qE and maximum
(b) 2qE and minimum
(c) qE and minimum
(d) zero and minimum
Show Answer & Explanation

Answer: (d) zero and minimum

Explanation:
1. In a uniform field the net force on a dipole is zero.
2. When p ∥ E the potential energy −pE is the minimum.

Teacher's Note:
1. Aligned is stable.

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