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In the following question a statement of...

In the following question a statement of assertion (A) is followed by a statement of reason (R )
A : Two large conducting spheres carrying charges `Q_(1) and Q_(2)` are brought close to each other. The magnitude of electrostatic force between them is exactly given by `Q_(1) Q_(2)// 4 pi epsilon_(0) r^(2)` , where r is the distance between their centres.
R: Here charges `Q_(1) and Q_(2)` can be assumed to be concentrated at the centres of their respective spheres.

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).

B

If both Assertion & Reason are true but the reason is not correct explanation of the assertion then mark (2)

C

If Assertion is true statement but Reason is false, then mark (3)

D

If both Assertion and Reason are false statements , then mark (4).

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the assertion (A) and the reason (R) provided in the question. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states that when two large conducting spheres with charges \( Q_1 \) and \( Q_2 \) are brought close together, the electrostatic force \( F \) between them can be calculated using the formula: \[ F = \frac{Q_1 Q_2}{4 \pi \epsilon_0 r^2} \] - Here, \( r \) is the distance between the centers of the two spheres. 2. **Understanding the Reason (R)**: - The reason states that the charges \( Q_1 \) and \( Q_2 \) can be assumed to be concentrated at the centers of their respective spheres. - This assumption is valid for large conducting spheres because, due to the symmetry of the charge distribution in conductors, the electric field outside the sphere behaves as if all the charge is concentrated at the center. 3. **Evaluating the Assertion**: - The formula provided in the assertion is indeed correct for calculating the electrostatic force between two point charges or spherical conductors when they are far apart relative to their sizes. - Since the spheres are large, the distance \( r \) can be considered as the distance between their centers. 4. **Evaluating the Reason**: - The reason correctly explains why the assertion holds true. For large conducting spheres, the charge distribution allows us to treat the charges as point charges located at their centers. 5. **Conclusion**: - Both the assertion (A) and the reason (R) are correct. - The reason provided effectively supports the assertion. ### Final Answer: Both the assertion and reason are correct. The reason explains the assertion.
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