Electric Charges and Fields Class 12 Case-Based Questions

Electric Charges and Fields — Class 12 Physics Case-Based Questions
Competency-focused practice based on electric charge, Coulomb's law, electric field, electric dipole, electric flux and Gauss's theorem.

How to Attempt Case-Based Questions

Read the situation carefully, identify the physical principle involved, and then use the relevant relation. For numerical sub-questions, show the essential calculation and unit. These cases are designed to test application and interpretation rather than simple recall.

Case Study 1 — Electrostatic Force and Superposition

Three point charges are placed at different positions in space. The force on any one charge is affected by every other charge present. The resultant force is obtained by considering the individual electrostatic forces and adding them vectorially.

1. Which principle is used to determine the net electrostatic force on a charge due to several other charges?
   A. Conservation of energy only
   B. Principle of superposition
   C. Lenz's law
   D. Faraday's law

   Answer: B

2. If the distance between two point charges is doubled while their magnitudes remain unchanged, the force becomes:
   A. Four times
   B. Twice
   C. One-half
   D. One-fourth

   Answer: D

3. Why must the individual forces be added as vectors?
   A. Force has both magnitude and direction
   B. Charge has no sign
   C. Distance is a scalar
   D. Coulomb's constant is a vector

   Answer: A

4. Two identical positive charges are placed symmetrically about a point. What can happen to the resultant electric field at the symmetry point?
   A. It must always be infinite
   B. The equal and opposite field vectors can cancel
   C. It must always point toward one charge
   D. It cannot be determined from symmetry

   Answer: B

Case Study 2 — Electric Field and Field Lines

An isolated positive point charge produces an electric field around itself. The field can be represented graphically using electric field lines. The density and direction of these lines provide information about the field.

1. The direction of the electric field due to a positive point charge is:
   A. Radially inward
   B. Radially outward
   C. Tangential to a circle
   D. Always upward

   Answer: B

2. Electric field intensity at a point is defined as:
   A. Force per unit positive test charge
   B. Charge per unit force
   C. Work per unit mass
   D. Energy per unit charge only

   Answer: A

3. Why do electric field lines not intersect one another?
   A. They are physical wires
   B. Electric field has a unique direction at a point
   C. Charges cannot move
   D. Field lines have no direction

   Answer: B

4. If the field lines are closer together in one region than another, the closer spacing indicates:
   A. A weaker field
   B. A stronger field
   C. Zero field
   D. Zero charge everywhere

   Answer: B

Case Study 3 — Electric Dipole in a Uniform Field

An electric dipole consists of two equal and opposite charges separated by a small distance. When placed in a uniform electric field, the two charges experience forces that can produce a torque. The torque depends on the dipole moment, electric field and angle between them.

1. The direction of electric dipole moment is from:
   A. Positive charge to negative charge
   B. Negative charge to positive charge
   C. Centre toward negative charge only
   D. The direction of the electric field only

   Answer: B

2. The magnitude of torque on a dipole in a uniform electric field is:
   A. pE cos θ
   B. pE sin θ
   C. p/E
   D. E/p

   Answer: B

3. For a dipole parallel to the electric field, the torque is:
   A. Maximum
   B. Zero
   C. Infinite
   D. Equal to pE

   Answer: B

4. For a dipole perpendicular to the electric field, the magnitude of torque is:
   A. Zero
   B. pE
   C. p/E
   D. E/p

   Answer: B

Case Study 4 — Electric Flux Through a Surface

A plane surface is placed in a uniform electric field. Electric flux through the surface depends on the magnitude of the field, the area and the angle between the electric field and the area vector.

1. The expression for electric flux through a plane surface in a uniform field is:
   A. EA sin θ
   B. EA cos θ
   C. E/A
   D. A/E

   Answer: B

2. Flux is maximum when the electric field is:
   A. Parallel to the area vector
   B. Perpendicular to the area vector
   C. At 90° to the surface normal only
   D. Zero

   Answer: A

3. If the electric field is parallel to the surface, the angle between E and the area vector is 90°. The flux is therefore:
   A. EA
   B. EA/2
   C. Zero
   D. Infinite

   Answer: C

4. A field of 2 × 10⁴ N/C passes normally through an area of 0.50 m². The flux is:
   A. 1 × 10⁴ N m²/C
   B. 4 × 10⁴ N m²/C
   C. 1 × 10⁻⁴ N m²/C
   D. 2.5 × 10⁴ N m²/C

   Answer: A

Case Study 5 — Gauss's Law and Spherical Symmetry

A thin uniformly charged spherical shell is surrounded by an imaginary closed Gaussian surface. Gauss's law connects the total electric flux through a closed surface with the net charge enclosed by that surface. The spherical symmetry makes the field calculation particularly convenient.

1. Gauss's law states that the total electric flux through a closed surface is:
   A. q_enclosedε₀
   B. q_enclosed/ε₀
   C. ε₀/q_enclosed
   D. Always zero

   Answer: B

2. For a Gaussian surface completely inside a uniformly charged thin spherical shell, the enclosed charge is:
   A. The total charge of the shell
   B. Half the shell charge
   C. Zero
   D. Infinite

   Answer: C

3. Therefore, the electric field inside the uniformly charged thin spherical shell is:
   A. Zero
   B. Constant and non-zero
   C. Proportional to r
   D. Proportional to 1/r

   Answer: A

4. At an external point, the field due to a uniformly charged spherical shell has the same form as the field of:
   A. A point charge equal to the total shell charge at the centre
   B. A line charge
   C. An infinite plane sheet
   D. A magnetic dipole

   Answer: A

Case Study 6 — Infinite Line Charge

An infinitely long straight wire carries a uniform linear charge density λ. A cylindrical Gaussian surface is selected coaxially with the wire so that the symmetry of the electric field can be used.

1. The appropriate Gaussian surface for an infinite straight line charge is:
   A. A sphere centred anywhere
   B. A cylinder coaxial with the wire
   C. A cube with arbitrary orientation
   D. A flat disc only

   Answer: B

2. The electric field due to an infinite line charge varies with distance r as:
   A. r
   B. r²
   C. 1/r
   D. 1/r²

   Answer: C

3. The magnitude of the field for linear charge density λ is:
   A. λ/(2πε₀r)
   B. λ/(4πε₀r²)
   C. 2πε₀λr
   D. λr/ε₀

   Answer: A

Case Study 7 — Infinite Plane Sheet

An infinite uniformly charged plane sheet has surface charge density σ. Because of its planar symmetry, the electric field has the same magnitude at equal distances on either side of the sheet.

1. The electric field due to an ideal infinite uniformly charged plane sheet is:
   A. σ/(2ε₀)
   B. σ/(4πε₀r²)
   C. σr/(2ε₀)
   D. Zero everywhere

   Answer: A

2. For an ideal infinite plane sheet, the field magnitude is:
   A. Dependent on distance from the sheet
   B. Independent of distance from the sheet
   C. Proportional to r²
   D. Inversely proportional to r²

   Answer: B

3. The electric field due to a positively charged infinite plane sheet is directed:
   A. Towards the sheet on both sides
   B. Away from the sheet on both sides
   C. Along the sheet
   D. In circular paths

   Answer: B

Case Study 8 — Mixed Competency Challenge

A student is revising the chapter by comparing different electrostatic situations: a point charge, an electric dipole, a closed Gaussian surface and extended charge distributions. The student must select the appropriate concept and relation for each situation.

1. Which quantity is a vector?
   A. Electric field
   B. Electric flux
   C. Electric charge
   D. Electric potential

   Answer: A

2. Which relation gives the torque on an electric dipole in a uniform field?
   A. τ = pE sin θ
   B. τ = p/E
   C. τ = E/p
   D. τ = p + E

   Answer: A

3. If the net charge enclosed by a closed Gaussian surface is zero, the net electric flux through the surface is:
   A. Always positive
   B. Always negative
   C. Zero
   D. Infinite

   Answer: C

4. Which standard Gauss-law application has an electric field magnitude independent of distance from the source plane?
   A. Infinite uniformly charged plane sheet
   B. Point charge
   C. Infinite line charge
   D. Dipole at a general point

   Answer: A

Quick Case-Based Revision

• Coulomb's law: inverse-square dependence for two point charges.
• Superposition: add individual electric forces or fields vectorially.
• Electric field: force per unit positive test charge.
• Dipole: equal and opposite charges separated by a small distance; p = qd.
• Torque: τ = pE sin θ.
• Flux: Φ = EA cos θ for a uniform field through a plane surface.
• Gauss's law: Φ = q_enclosed/ε₀.
• Infinite line charge: E ∝ 1/r.
• Infinite plane sheet: E = σ/(2ε₀), independent of distance for the ideal infinite sheet.
• Thin spherical shell: field is zero inside; outside it has the point-charge form.

Exam Checklist

• Identify the physical principle before selecting a formula.
• Check whether the question concerns a vector or scalar quantity.
• For flux, identify the angle with the area vector.
• For Gauss's law, focus on the charge enclosed by the closed surface.
• Use symmetry to choose an appropriate Gaussian surface.
• For application questions, explain the reason instead of giving only the option.

Curriculum basis: CBSE Class XII Physics 2026–27, Unit I: Electrostatics, Chapter 1: Electric Charges and Fields. The official syllabus includes electric charge, Coulomb's law, superposition, electric field, electric dipole, electric flux and Gauss's theorem with applications to an infinite straight wire, infinite plane sheet and thin spherical shell. citeturn0search9