CUET UG Physics Electrostatics Electric Charges Coulombs Law Superposition Principle

Must-Know (15–20 detailed bullets)

• Electric charge is quantized; the smallest unit is the charge of an electron: ( e = 1.6 \times 10^{-19} \, \text{C} ). Any charge ( q ) is given by ( q = \pm ne ), where ( n ) is an integer. Example: ( q = 3.2 \times 10^{-19} \, \text{C} ) corresponds to ( n = 2 ).

• Like charges repel, unlike charges attract — fundamental property of electric charges.

• Electric charge is conserved in an isolated system. In pair production, a gamma photon creates an electron and a positron: total charge before (0) equals total charge after (( -e + e = 0 )).

• Coulomb’s Law: The force between two point charges ( q_1 ) and ( q_2 ) separated by distance ( r ) is ( F = \frac{1}{4\pi\varepsilon_0} \frac{|q_1 q_2|}{r^2} ), where ( \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 ).

• The direction of the electrostatic force acts along the line joining the two charges; it is repulsive for like charges, attractive for unlike.

• Permittivity of free space: ( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} ); used in Coulomb’s constant.

• Coulomb force is much stronger than gravitational force. For two electrons, ( \frac{F_{\text{electrostatic}}}{F_{\text{gravitational}}} \approx 10^{42} ).

• The electrostatic force obeys Newton’s third law: ( \vec{F}{12} = -\vec{F} ), even if ( q_1 \ne q_2 ).

• Superposition Principle: Net force on a charge due to multiple charges is the vector sum of individual forces. For three charges ( q_1, q_2, q_3 ), force on ( q_1 ) is ( \vec{F}1 = \vec{F} ).} + \vec{F}_{13

• Electric field due to a point charge ( q ) at distance ( r ): ( E = \frac{1}{4\pi\varepsilon_0} \frac{|q|}{r^2} ); direction is radially outward for positive, inward for negative.

• Electric field is a vector quantity; SI unit is N/C or V/m.

• Electric field lines start from positive charges and end on negative charges; they never form closed loops.

• Number of field lines is proportional to magnitude of charge; two charges of ( +2q ) and ( -q ) will have twice as many lines emerging from ( +2q ) as terminating on ( -q ).

• Field lines never intersect; if they did, it would imply two directions of field at a point.

• In a uniform electric field, a dipole experiences torque ( \tau = pE \sin\theta ), but no net force.

• Electric dipole moment: ( \vec{p} = q \times 2\vec{a} ), where ( 2a ) is the separation between ( +q ) and ( -q ); direction from negative to positive.

• Dipole in external field: potential energy ( U = -\vec{p} \cdot \vec{E} = -pE \cos\theta ). Minimum energy at ( \theta = 0^\circ ), maximum at ( \theta = 180^\circ ).

• Continuous charge distribution types: linear (( \lambda = dq/dl )), surface (( \sigma = dq/dA )), volume (( \rho = dq/dV )).

• Charge is invariant under motion; the charge of an electron is ( 1.6 \times 10^{-19} \, \text{C} ) whether at rest or moving.

• Verify from NCERT: Exact value of Coulomb’s constant in different media (depends on relative permittivity ( \varepsilon_r )).

Difficulty Level

Intermediate — requires understanding of vector addition and inverse-square law, but formulas are direct from NCERT.

Common CUET Traps

• Trap: Assuming Coulomb’s law applies directly to extended bodies without considering point charge approximation.
  Avoid: Coulomb’s law is strictly for point charges; for extended objects, use integration or symmetry.

• Trap: Forgetting that force is a vector and adding magnitudes directly in superposition.
  Avoid: Always resolve forces into components and perform vector addition.

• Trap: Thinking electric field lines represent path of a charged particle.
  Avoid: Field lines indicate direction of force on a positive test charge, not trajectory.

Practice MCQs

Q1. Two point charges ( +3 \mu\text{C} ) and ( +8 \mu\text{C} ) repel each other with a force of 40 N. If each is given an additional charge of ( -1 \mu\text{C} ), what will be the new force?
A. 20 N
B. 24 N
C. 30 N
D. 36 N

Answer: B
Explanation: New charges are ( +2 \mu\text{C} ) and ( +7 \mu\text{C} ); ratio of forces ( F_2/F_1 = (2 \times 7)/(3 \times 8) = 14/24 = 7/12 ); ( F_2 = 40 \times 7/12 \approx 23.33 \approx 24 \, \text{N} ).
Why others fail: Option D (36 N) comes from incorrectly assuming linear change in charge.

Q2. What is the magnitude of the force between two point charges of ( 1\, \text{C} ) each separated by 1 m in vacuum?
A. ( 9 \times 10^8 \, \text{N} )
B. ( 9 \times 10^9 \, \text{N} )
C. ( 1.6 \times 10^{-19} \, \text{N} )
D. ( 8.85 \times 10^{-12} \, \text{N} )

Answer: B
Explanation: Using ( F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2} = 9 \times 10^9 \times \frac{1 \times 1}{1^2} = 9 \times 10^9 \, \text{N} ).
Why others fail: Option A is off by a power of 10; common calculation error.

Q3. Three charges ( +q ), ( +q ), and ( -q ) are placed at the vertices of an equilateral triangle. The net force on the charge at the top vertex (assumed positive) will be directed:
A. Vertically upward
B. Vertically downward
C. Horizontally left
D. Horizontally right

Answer: C
Explanation: The two equal positive charges repel, the negative attracts; vector sum results in net force toward the negative charge (left).
Why others fail: Option B arises from incorrectly summing vertical components only.

Q4. Two point charges ( +4q ) and ( +q ) are placed at a distance ( d ) apart. A third charge ( Q ) is placed at the midpoint. For the net force on ( Q ) to be zero, ( Q ) must be:
A. Positive
B. Negative
C. Zero
D. Any value

Answer: C
Explanation: Forces from ( +4q ) and ( +q ) on any charge ( Q ) at midpoint are in opposite directions but unequal in magnitude (( F \propto 4q/d^2 ) vs ( q/d^2 )), so cannot cancel unless ( Q = 0 ).
Why others fail: Option D assumes symmetry, but charges are unequal.

Q5. A dipole of dipole moment ( 5 \times 10^{-7} \, \text{C·m} ) is placed in a uniform electric field of ( 2 \times 10^4 \, \text{N/C} ) making an angle of ( 30^\circ ) with the field. The torque experienced is:
A. ( 5 \times 10^{-3} \, \text{N·m} )
B. ( 10^{-2} \, \text{N·m} )
C. ( 5 \times 10^{-4} \, \text{N·m} )
D. ( 2.5 \times 10^{-3} \, \text{N·m} )

Answer: A
Explanation: ( \tau = pE \sin\theta = (5 \times 10^{-7})(2 \times 10^4) \sin 30^\circ = (10^{-2})(0.5) = 5 \times 10^{-3} \, \text{N·m} ).
Why others fail: Option D comes from using ( \cos 30^\circ ) instead of ( \sin 30^\circ ).

Last‑Minute Revision (15–20 one-liners)

• ⚠️ Charge is quantized: ( q = ne ), ( e = 1.6 \times 10^{-19} \, \text{C} ).
• ⚠️ Coulomb’s constant: ( 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 ).
• ⚠️ ( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} ).
• ⚠️ Like charges repel, unlike attract — fundamental behavior.
• ⚠️ Electrostatic force >> gravitational force between charged particles.
• ⚠️ Superposition principle: vector sum of forces.
• ⚠️ Electric field due to ( +q ): radially outward; ( -q ): radially inward.
• ⚠️ SI unit of electric field: N/C or V/m.
• ⚠️ Electric field lines never intersect.
• ⚠️ Field lines start at +ve, end at -ve charges.
• ⚠️ Number of field lines ∝ magnitude of charge.
• ⚠️ Dipole moment ( \vec{p} = q \times 2\vec{a} ), direction –ve to +ve.
• ⚠️ Torque on dipole: ( \tau = pE \sin\theta ).
• ⚠️ Potential energy of dipole: ( U = -pE \cos\theta ).
• ⚠️ Net force on dipole in uniform field is zero.
• ⚠️ In non-uniform field, dipole experiences both torque and net force.
• ⚠️ Linear charge density ( \lambda = dq/dl ).
• ⚠️ Surface charge density ( \sigma = dq/dA ).
• ⚠️ Volume charge density ( \rho = dq/dV ).
• ⚠️ Charge is conserved, quantized, and invariant.