A-Level Physics October/November 2024 Q5(b): Explain why it is not possible for the total electric potential and the resultant elect…

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  To analyse the conditions for zero potential and zero field, we must consider the nature of each quantity and the signs of the charges required.

  1. Condition for Zero Total Electric Potential ($V_T = 0$)

  • Electric potential is a scalar quantity. The total potential at point P is the algebraic sum of the individual potentials from each charge: $V_T = V_X + V_Y$.
  • For $V_T$ to be zero, one potential must be positive and the other must be negative ($V_X = -V_Y$).
  • Since potential is given by $V = \frac{Q}{4\pi\epsilon_0 r}$ and the distance $r$ is always positive, this requires the two charges, $Q_X$ and $Q_Y$, to have opposite signs.

  2. Condition for Zero Resultant Electric Field ($E_{res} = 0$)

  • Electric field is a vector quantity. The resultant field at point P is the vector sum of the individual fields: $\vec{E}_{res} = \vec{E}_X + \vec{E}_Y$.
  • For the resultant field to be zero at point P, which is located between the charges, the individual field vectors must be equal in magnitude and point in opposite directions.
  • If both charges are positive, the field from X points away (right) and the field from Y points away (left). They are in opposite directions. If both charges are negative, the field from X points towards it (left) and the field from Y points towards it (right). They are again in opposite directions.
  • Therefore, for the fields to be in opposite directions at a point between the charges, the two charges must have the same sign.

  3. Conclusion

  The condition for zero potential (charges have opposite signs) is mutually exclusive with the condition for zero field strength (charges have the same sign). It is not possible to satisfy both conditions simultaneously. Therefore, the total electric potential and the resultant electric field cannot both be zero at point P.

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  How the marks are awarded

  • B1 — Stating that for total potential to be zero, the charges must have opposite signs, because potential is a scalar and one must be positive and the other negative.
  • B1 — Stating that for the resultant field to be zero at a point between the charges, the charges must have the same sign, because this is the condition for the field vectors to be in opposite directions.
  • B1 — Making the concluding statement that these two conditions (opposite signs vs same signs) are contradictory, and therefore it is not possible for both potential and field to be zero simultaneously.

  Common mistakes

  • Confusing scalar and vector properties, e.g., stating that potentials must be in 'opposite directions' to cancel.
  • Incorrectly stating that opposite charges are needed for the electric field to be zero, failing to visualise that for a point between the charges, this would cause the field vectors to point in the same direction.
  • Giving a vague answer like 'potential is a scalar and field is a vector' without explaining how this leads to a contradiction regarding the signs of the charges.
  • Only explaining the condition for one of the quantities (e.g., potential) but not the other, and thus failing to establish the contradiction.

  Examiner tip: For 'explain why' questions involving multiple physical principles, analyse the conditions required for each principle separately before comparing them to find a contradiction or connection.

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