Electrostatic Potential & Capacitance

13 NEET-UG practice questions on Electrostatic Potential & Capacitance, part of Physics. The first 13 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
How much work is needed to assemble three charges, each of +1 µC, at the corners of an equilateral triangle of side 0.3 m, starting from far apart? Take 1/(4πε₀) = 9 × 10⁹ N m²/C².
1. A0.03 J
2. B0.18 J
3. C0.09 J
4. D0.06 J
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Answer: C · 0.09 J
Each pair contributes kq²/a = 9 × 10⁹ × 10⁻¹²/0.3 = 0.03 J. Three charges form 3 pairs, so the total = 0.09 J. Check: bringing the second charge costs 0.03 J and the third 0.06 J.
- A: This counts only one pair.
- B: This counts each pair twice.
- D: This counts only two pairs.
Remember this
The potential energy of a system is the sum over all pairs, each pair counted once.
Question 2 · Medium
A parallel plate capacitor is charged and then disconnected from the battery. A dielectric slab of constant K is then inserted to fill the whole gap. A. The capacitance becomes K times its value. B. The charge on the plates stays unchanged. C. The energy stored decreases. D. The potential difference between the plates increases. Which statements are correct?
1. AA, B and C only
2. BA, B and D only
3. CC and D only
4. DA and B only
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Answer: A · A, B and C only
Capacitance becomes KC. The isolated plates keep their charge Q. So V = Q/(KC) falls by K, and energy Q²/(2KC) falls by K, which makes C true and D false.
- B: D is false: V falls when C rises at fixed Q.
- C: This misses A and B and includes the false D.
- D: This misses C, since the energy Q²/2C falls.
Remember this
Battery removed: Q stays, V and U fall by K. Battery connected: V stays, Q and U rise by K.
Question 3 · Easy
Arrange these combinations of three identical capacitors, each of capacitance C, in increasing order of equivalent capacitance. A. All three in series B. Two in series, with the third in parallel to this pair C. Two in parallel, with the third in series with this pair D. All three in parallel
1. AA, C, D, B
2. BC, A, B, D
3. CA, C, B, D
4. DA, B, C, D
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Answer: C · A, C, B, D
A gives C/3. C gives (2C × C)/(3C) = 2C/3. B gives C/2 + C = 3C/2. D gives 3C. The increasing order is A, C, B, D.
- A: This ranks 3C below 3C/2.
- B: This ranks 2C/3 below C/3.
- D: This interchanges the two mixed combinations, 3C/2 and 2C/3.
Remember this
Series lowers capacitance below the smallest member; parallel simply adds the values.
Question 4 · Medium
A 4 µF capacitor charged to 100 V is connected in parallel to an uncharged 6 µF capacitor. How much energy is lost in the process?
1. A24 mJ
2. B12 mJ
3. C8 mJ
4. D20 mJ
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Answer: B · 12 mJ
Before: (1/2)(4 × 10⁻⁶)(100)² = 20 mJ. Common V = 400 µC/10 µF = 40 V, so after: (1/2)(10 × 10⁻⁶)(40)² = 8 mJ. Loss = 12 mJ. Check: (1/2)[C₁C₂/(C₁ + C₂)]V² = (1/2)(2.4 × 10⁻⁶)(100)² = 12 mJ.
- A: This leaves out the factor 1/2 in the loss formula.
- C: This is the energy left after sharing, not the loss.
- D: This is the energy before sharing.
Remember this
Charge is conserved on sharing, but energy is always lost, as (1/2)[C₁C₂/(C₁ + C₂)](V₁ − V₂)².
Question 5 · Hard
Capacitors of 2 µF and 3 µF are connected in series across a 100 V supply. After charging, they are removed and reconnected to each other with like-charged plates joined. What is the final common potential difference?
1. A48 V
2. BZero
3. C50 V
4. D100 V
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Answer: A · 48 V
In series, Ceq = 1.2 µF, so each capacitor holds Q = 120 µC (60 V and 40 V). With like plates joined, the total charge is 240 µC on 5 µF, so V = 48 V. Check: (2 × 60 + 3 × 40)/5 = 240/5 = 48 V.
- B: This is the result of joining unlike plates, where the equal charges cancel.
- C: This takes the plain mean of 60 V and 40 V.
- D: This assumes the capacitors keep the supply voltage.
Remember this
Series capacitors carry equal charge; like plates joined add charges, while unlike plates joined subtract them.
Question 6 · Easy
How is the electric field oriented at any point on an equipotential surface?
1. AAt 45° to the surface
2. BParallel to the nearest charge
3. CTangent to the surface
4. DNormal to the surface
Answer and explanation in LearnFree account
Question 7 · Medium
A conducting sphere of radius 10 cm carries a charge of 2 nC. Taking 1/(4πε₀) = 9 × 10⁹ N m²/C², what are the electric field and the potential at a point 5 cm from its centre?
1. A0 and 360 V
2. B7200 N/C and 360 V
3. C0 and 180 V
4. D1800 N/C and 180 V
Answer and explanation in LearnFree account
Question 8 · Hard
A 6 µF air-filled parallel plate capacitor is charged to 30 V and disconnected from the battery. A slab of dielectric constant 3, of thickness half the plate separation, is then placed between the plates. What is the new potential difference between the plates?
1. A20 V
2. B30 V
3. C15 V
4. D10 V
Answer and explanation in LearnFree account
Question 9 · Medium
A cell is connected to the capacitor network drawn here. Find the charge on the 3 µF capacitor in the steady state.
Figure: MedExams
1. A72 µC
2. B48 µC
3. C36 µC
4. D24 µC
Answer and explanation in LearnFree account
Question 10 · Easy
Equally spaced parallel equipotential surfaces of a uniform electric field are drawn in the figure. What are the magnitude and direction of the field?
Figure: MedExams
1. A200 V/m, from the 10 V surface towards the 40 V surface
2. B2 V/m, from the 40 V surface towards the 10 V surface
3. C200 V/m, from the 40 V surface towards the 10 V surface
4. D600 V/m, from the 40 V surface towards the 10 V surface
Answer and explanation in LearnFree account
Question 11 · Medium
Which plot gives the potential V at distance r from the centre of a thin metal shell of radius R holding charge +Q, far from all other bodies?
Figure: MedExams
1. AGraph C
2. BGraph A
3. CGraph D
4. DGraph B
Answer and explanation in LearnFree account
Question 12 · Hard
Two capacitors were charged separately to the voltages marked and then disconnected from their cells. Note the polarity of each. How much energy is lost as heat after switch S is closed and charges settle?
Figure: MedExams
1. A864 µJ
2. B108 µJ
3. C972 µJ
4. D384 µJ
Answer and explanation in LearnFree account
Question 13 · Medium
Without any slab, a parallel plate capacitor has a capacitance of 10 µF. A slab fills the gap as drawn, covering the whole plate area. What is the new capacitance?
Figure: MedExams
1. A16 µF
2. B25 µF
3. C8 µF
4. D40 µF
Answer and explanation in LearnFree account

Electrostatic Potential & Capacitance

How much work is needed to assemble three charges, each of +1 µC, at the corners of an equilateral triangle of side 0.3 m, starting from far apart? Take 1/(4πε₀) = 9 × 10⁹ N m²/C².

Arrange these combinations of three identical capacitors, each of capacitance C, in increasing order of equivalent capacitance. A. All three in series B. Two in series, with the third in parallel to this pair C. Two in parallel, with the third in series with this pair D. All three in parallel

A 4 µF capacitor charged to 100 V is connected in parallel to an uncharged 6 µF capacitor. How much energy is lost in the process?

Capacitors of 2 µF and 3 µF are connected in series across a 100 V supply. After charging, they are removed and reconnected to each other with like-charged plates joined. What is the final common potential difference?

How is the electric field oriented at any point on an equipotential surface?

A conducting sphere of radius 10 cm carries a charge of 2 nC. Taking 1/(4πε₀) = 9 × 10⁹ N m²/C², what are the electric field and the potential at a point 5 cm from its centre?

A 6 µF air-filled parallel plate capacitor is charged to 30 V and disconnected from the battery. A slab of dielectric constant 3, of thickness half the plate separation, is then placed between the plates. What is the new potential difference between the plates?

A cell is connected to the capacitor network drawn here. Find the charge on the 3 µF capacitor in the steady state.

Equally spaced parallel equipotential surfaces of a uniform electric field are drawn in the figure. What are the magnitude and direction of the field?

Which plot gives the potential V at distance r from the centre of a thin metal shell of radius R holding charge +Q, far from all other bodies?

Two capacitors were charged separately to the voltages marked and then disconnected from their cells. Note the polarity of each. How much energy is lost as heat after switch S is closed and charges settle?

Without any slab, a parallel plate capacitor has a capacitance of 10 µF. A slab fills the gap as drawn, covering the whole plate area. What is the new capacitance?