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Assertion : Due to two point charges ele...

Assertion : Due to two point charges electric field and electric potential can't be zero at some point simultaneously.
Reason : Field is a vector quantity and potential a scalar quantity.

A

If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided: **Assertion**: Due to two point charges, electric field and electric potential can't be zero at some point simultaneously. **Reason**: Field is a vector quantity and potential is a scalar quantity. ### Step-by-Step Solution: 1. **Understanding Electric Potential**: - The electric potential (V) due to a point charge (Q) at a distance (R) is given by the formula: \[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R} \] - For two point charges \( Q_1 \) and \( Q_2 \) located at distances \( R_1 \) and \( R_2 \) respectively, the total electric potential at a point is: \[ V_{\text{total}} = V_1 + V_2 = \frac{1}{4 \pi \epsilon_0} \left( \frac{Q_1}{R_1} + \frac{Q_2}{R_2} \right) \] - For the total potential to be zero, the contributions from both charges must cancel each other out. This can only happen if the charges are of opposite signs. 2. **Understanding Electric Field**: - The electric field (E) due to a point charge is given by: \[ E = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R^2} \] - The electric field due to two point charges \( Q_1 \) and \( Q_2 \) at a point is the vector sum of the fields due to each charge: \[ E_{\text{total}} = E_1 + E_2 \] - The direction of the electric field is away from positive charges and towards negative charges. 3. **Analyzing the Assertion**: - If we have two point charges of opposite signs, it is possible for the electric potential to be zero at some point. However, the electric field due to these charges will not be zero at that point because the fields from both charges will not cancel each other out completely (as they are vectors and have different directions). - Thus, the assertion that electric field and electric potential cannot be zero at the same point is correct. 4. **Analyzing the Reason**: - The reason states that electric field is a vector quantity and potential is a scalar quantity. This is true, but it does not directly explain why electric field and potential cannot be zero simultaneously. - The distinction between vector and scalar quantities is relevant, but it doesn't provide a justification for the assertion. 5. **Conclusion**: - Both the assertion and reason are true, but the reason does not correctly explain the assertion. Therefore, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation of the assertion. ### Final Answer: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
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