Potential Difference

Answer: B. NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.4 (page 47): V_P − V_R is the work done by an external force in bringing a unit positive charge from R to P.

Why A is wrong: A is wrong because it reverses the order: moving from P to R gives V_R − V_P, which has the opposite sign.

Why C is wrong: C is wrong because the work done by the field is the negative of the work done by the external force (page 46), so it equals V_R − V_P, not V_P − V_R.

Why D is wrong: D is wrong because the work for a charge q is q times the potential difference; potential difference is work per unit positive charge, independent of q.

Answer: A. NCERT Class 12 Physics Part I, Chapter 2, Section 2.6.1 (page 55): the electric field is in the direction in which the potential decreases steepest.

Why B is wrong: B is wrong because it reverses the direction: moving along the field, V falls; it does not rise.

Why C is wrong: C is wrong because the field lies along the direction of steepest decrease of V; it is perpendicular only to surfaces of constant potential, along which V does not change.

Why D is wrong: D is wrong because NCERT links them directly: the field points toward decreasing potential, with magnitude equal to the rate of change of V with distance.

Answer: B. NCERT Class 12 Physics Part I, Chapter 2, page 46: the work done by an electrostatic field in moving a charge from one point to another depends only on the initial and final points and is independent of the path.

Why A is wrong: A is wrong because no path is special: every path between the same two points gives the same work.

Why C is wrong: C is wrong because path-independence is the defining feature of a conservative force; path length does not enter.

Why D is wrong: D is wrong because a conservative field does zero work only around a closed path (same start and end point); between two different points the work is −q(V_B − V_A), which is generally non-zero.

Answer: D. W_ext = q(V_B − V_A) = (2.0 × 10⁻⁶ C)(50 V − 10 V) = 2.0 × 10⁻⁶ × 40 = 8.0 × 10⁻⁵ J (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.4, page 47).

Why A is wrong: A is wrong because 80 J = 2.0 × 40 drops the micro prefix; 2.0 µC is 2.0 × 10⁻⁶ C.

Why B is wrong: B is wrong because −8.0 × 10⁻⁵ J = q(V_A − V_B) = 2.0 × 10⁻⁶ × (−40); it reverses the order of the difference, which gives the work done by the field, not by the external agent.

Why C is wrong: C is wrong because 1.2 × 10⁻⁴ J = 2.0 × 10⁻⁶ × (50 + 10) adds the two potentials instead of subtracting them.

Answer: C. W_field = −q(V_f − V_i) = −(−1.6 × 10⁻¹⁹ C)(120 V − 20 V) = +1.6 × 10⁻¹⁹ × 100 = +1.6 × 10⁻¹⁷ J. A negative charge moving to higher potential has positive work done on it by the field (NCERT Chapter 2, Eq. 2.4, page 47; page 46 for field work = −external work).

Why A is wrong: A is wrong because −1.6 × 10⁻¹⁷ J comes from dropping the negative sign of the electron's charge (using +1.6 × 10⁻¹⁹ C), which flips the sign of the work.

Why B is wrong: B is wrong because 2.24 × 10⁻¹⁷ J = 1.6 × 10⁻¹⁹ × (120 + 20) adds the potentials instead of taking their difference.

Why D is wrong: D is wrong because 1.92 × 10⁻¹⁷ J = 1.6 × 10⁻¹⁹ × 120 uses only the final potential instead of the potential difference of 100 V.

Answer: D. W_ext = q(V_Q − V_P) = (−3.0 × 10⁻⁶ C)(−20 V − 40 V) = (−3.0 × 10⁻⁶)(−60) = +1.8 × 10⁻⁴ J (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.4, page 47).

Why A is wrong: A is wrong because −1.8 × 10⁻⁴ J = (−3.0 × 10⁻⁶)(40 − (−20)) = (−3.0 × 10⁻⁶)(+60) reverses the order to V_P − V_Q.

Why B is wrong: B is wrong because +1.2 × 10⁻⁴ J = 3.0 × 10⁻⁶ × 40 uses only the potential at P and ignores the sign of the charge.

Why C is wrong: C is wrong because −6.0 × 10⁻⁵ J = (−3.0 × 10⁻⁶)(−20 + 40) adds the two potentials instead of subtracting them.

Answer: A. Step 1: work by the field = −q(V_f − V_i) = −(1.6 × 10⁻¹⁹)(200 − 500) = +1.6 × 10⁻¹⁹ × 300 = +4.8 × 10⁻¹⁷ J. Step 2: starting from rest, the kinetic energy gained equals this work, so KE = 4.8 × 10⁻¹⁷ J. A positive charge released from rest moves toward lower potential (NCERT Chapter 2, pages 46–47).

Why B is wrong: B is wrong because it reverses the energy direction: a positive charge loses potential energy qV when it moves to lower V, and that loss appears as kinetic energy.

Why C is wrong: C is wrong because 8.0 × 10⁻¹⁷ J = 1.6 × 10⁻¹⁹ × 500 uses only the starting potential instead of the 300 V difference.

Why D is wrong: D is wrong because 1.12 × 10⁻¹⁶ J = 1.6 × 10⁻¹⁹ × (500 + 200) adds the potentials instead of subtracting them.

Answer: C. The field points toward lower potential (NCERT Chapter 2, Section 2.6.1, page 55), so V_N < V_M and V_N − V_M is negative. Work by the field = −q(V_N − V_M) = −(negative)(negative) = negative. Physically, the force on a negative charge is opposite to the field, so moving it along the field is against the force.

Why A is wrong: A is wrong because it gets V_N − V_M negative correctly but treats the charge as positive: −(positive)(negative) = positive. That is the result for a positive charge, not a negative one.

Why B is wrong: B is wrong because it takes the field as pointing toward higher potential, so V_N − V_M comes out positive, and then −q(V_N − V_M) = −(negative)(positive) = positive.

Why D is wrong: D is wrong because it both takes the field as pointing toward higher potential (V_N − V_M positive) and treats the charge as positive: −(positive)(positive) = negative. The final sign matches only because two errors cancel.