Question 1
Find the force between charges 2×10⁻⁷ C and 3×10⁻⁷ C separated by 30 cm in air.
Steps only
F=kq₁q₂/r²=6.0×10⁻³ N
Answer
6.0 mN, repulsive
CLASS 12 · PHYSICS · CHAPTER 1
Electric charges and fields
Accessible, step-by-step answers to all 23 current exercises on charge, Coulomb's law, electric fields, flux and Gauss's law.
23 worked answersComplete chapter answers
23 worked answers · short steps first, explanations when you need them
Chapter 1 Exercises
Textbook pages 42–44
Question 2
A +0.4 μC sphere attracts a −0.8 μC sphere with force 0.2 N. Find their separation and the force on the second sphere.
Steps only
r=√(k|q₁q₂|/F)=0.12 m; the force on the second has equal magnitude and opposite direction.
Answer
0.12 m; 0.2 N attraction
Question 3
Show that ke²/(Gmₑmₚ) is dimensionless, estimate its value and explain its meaning.
Steps only
The force ratio cancels r² and units; its value is about 2.3×10³⁹.
Answer
Dimensionless; electric force is about 2.3×10³⁹ times stronger.
Question 4
(a) What does it mean that charge is quantised? (b) Why can this be ignored for large bodies?
Steps only
q=ne. Since e is very small, the discrete steps are negligible on a large scale.
Answer
Charge is in integer multiples of e; macroscopic steps look continuous.
Question 5
Explain how rubbing a glass rod with silk is consistent with conservation of charge.
Steps only
Electrons move from glass to silk: one body's charge gain balances the other's loss.
Answer
Total charge is conserved.
Question 6
Charges +2 μC, −5 μC, +2 μC and −5 μC sit at square corners A, B, C and D. Find the force on +1 μC at the centre; side=10 cm.
Steps only
Opposite corners carry equal charges, so each opposite pair's forces cancel at the centre.
Answer
0 N
Question 7
(a) Why can an electrostatic field line not stop suddenly? (b) Why can two field lines not cross?
Steps only
Field lines end only on charges; a crossing would assign two field directions at one point.
Answer
They cannot break in empty space or cross.
Question 8
Charges +3 μC and −3 μC are 20 cm apart. Find the field at the midpoint and the force on a −1.5×10⁻⁹ C test charge there.
Steps only
E=2kq/(0.10)²=5.4×10⁶ N/C; F=qE has magnitude 8.1×10⁻³ N and points opposite E.
Answer
5.4×10⁶ N/C; force=8.1 mN opposite E
Question 9
Charges +2.5×10⁻⁷ C and −2.5×10⁻⁷ C are at z=−15 cm and z=+15 cm. Find total charge and dipole moment.
Steps only
Qtotal=0; p=qd=2.5×10⁻⁷×0.30=7.5×10⁻⁸ C m, from − to + (−z).
Answer
0 C; 7.5×10⁻⁸ C m along −z
Question 10
A dipole of moment 4×10⁻⁹ C m makes 30° with a 5×10⁴ N/C uniform electric field. Find the torque magnitude.
Steps only
τ=pE sin30°=1.0×10⁻⁴ N m
Answer
1.0×10⁻⁴ N m
Question 11
Polythene gains charge −3×10⁻⁷ C when rubbed with wool. How many electrons moved, in which direction, and was mass transferred?
Steps only
n=|q|/e≈1.9×10¹²; mass=nmₑ≈1.7×10⁻¹⁸ kg.
Answer
Electrons and a tiny mass transfer from wool to polythene.
Question 12
Two equal charges 6.5×10⁻⁷ C are 0.50 m apart. Find their repulsive force. What if both charges double and the distance halves?
Steps only
F₁=kq²/r²=0.0152 N; F₂=16F₁≈0.243 N
Answer
0.0152 N; then 0.243 N
Question 13
In the uniform-field track diagram, identify the signs of particles 1, 2 and 3, and the particle with greatest |q|/m.
Steps only
Deflection is opposite E for negative charges and along E for positive charges; the greatest bend indicates greatest |q|/m.
Answer
1,2 negative; 3 positive; particle 3 has greatest |q|/m.
Question 14
A 3×10³ N/C field points along +x. Find flux through a 10 cm square (a) parallel to yz and (b) with its normal at 60° to +x.
Steps only
Φ=EAcosθ; A=0.010 m²; values are 30 and 15 N m²/C.
Answer
30; 15 N m²/C
Question 15
Find the net flux of the uniform field from Exercise 1.14 through a cube, side 20 cm, with faces parallel to coordinate planes.
Steps only
For a uniform field and no enclosed charge, opposite-face fluxes cancel.
Answer
0 N m²/C
Question 16
A closed surface has outward electric flux 8.0×10³ N m²/C. Find enclosed charge. Would zero flux prove there are no enclosed charges?
Steps only
q=ε₀Φ=7.1×10⁻⁸ C; zero net flux does not rule out equal positive and negative charges.
Answer
7.1×10⁻⁸ C; no
Question 17
A +10 μC charge is 5 cm above the centre of a 10 cm square. Find the magnitude of flux through the square.
Steps only
Φ=q/(6ε₀)=10×10⁻⁶/(6×8.854×10⁻¹²)=1.88×10⁵ N m²/C
Answer
1.88×10⁵ N m²/C
Question 18
A 2.0 μC point charge is at the centre of a cube. Find the net flux through the cube.
Steps only
Φ=q/ε₀=2.0×10⁻⁶/(8.854×10⁻¹²)=2.26×10⁵ N m²/C
Answer
2.26×10⁵ N m²/C
Question 19
A centred point charge gives flux −1.0×10³ N m²/C through a sphere. What if the sphere radius doubles, and what is the charge?
Steps only
Φ is radius-independent; q=ε₀Φ=−8.85×10⁻⁹ C.
Answer
Same flux; −8.85 nC
Question 20
A conducting sphere has E=1.5×10³ N/C directed inward at a point 20 cm from its centre. Find its charge.
Steps only
q=−Er²/k=−(1.5×10³)(0.20)²/(9×10⁹)=−6.7×10⁻⁹ C
Answer
−6.7 nC
Question 21
A conducting sphere 2.4 m in diameter has surface charge density 80.0 μC/m². Find its charge and outward electric flux.
Steps only
q=σ4πR²≈1.45×10⁻³ C; Φ=q/ε₀≈1.64×10⁸ N m²/C
Answer
1.45 mC; 1.64×10⁸ N m²/C
Question 22
An infinite line charge produces 9×10⁴ N/C at a perpendicular distance of 2 cm. Find its linear charge density.
Steps only
λ=2πε₀rE≈1.0×10⁻⁷ C/m
Answer
1.0×10⁻⁷ C/m
Question 23
Two close parallel metal plates have opposite inner-face charge densities of magnitude 17.0×10⁻²² C/m². Find E outside each plate and between them.
Steps only
The outer fields cancel; the fields add between the plates: E=σ/ε₀.
Answer
Outside: 0; between: 1.92×10⁻¹⁰ N/C