Assertion :Electric potential on the surface of a charged sphere of radius R is V. Then electric field at a distance $r = \frac{R}{2}$ from centre is $\frac{V}{2 R}$ Charge is distributed uniformly over the volume. Reason: From centre to surface, electric field varies linearly with r. Here, r is distance from centre.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Using Gauss' law, the electric field inside the sphere is:
$E = k \frac{(Q r^{3} / R^{3})}{r^{2}} = k Q r / R^{3}$ , where $k = 1 / 4 π ϵ_{o}$ .
Thus, inside sphere, electric field varies linearly with $r$ .
Now if potential at the surface is $V$ then electric field is $V r / R^{2}$ . So It should be $V / 2 R$ if distance from the center is $R / 2$ .
Thus, both assertion and reason are true but reason is not the correct explanation of the assertion.

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Similar questions

Q. Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.

Reason (R)
Volume of a sphere =

\frac{4}{3} π R^{3}

Surface area of a sphere =

4 π R^{2}

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
The curved surface area of a cone of base radius 3 cm and height 4 cm is 15π cm².

Reason (R)
Volume of a cone = πr²h

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I f t h e v o l u m e s o f t w o s p h e r e s a r e & V o l u m e o f a s p h e r e s = \frac{4}{3} π R^{3} . i n t h e r a t i o 27 : 8 t h e n t h e i r s u r f a c e a r e a s a r e i n t h e r a t i o 3 : 2 & S u r f a c e a r e a o f a s p h e r e = 4 π R^{2} . \end{matrix}$

The correct answer is (a) / (b) / (c) / (d).

Q. Assertion (A)
The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm²is Rs 2300.

Reason (R)
The total surface area of a hemisphere is 3π r².

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

The correct answer is :(a) /(b) /(c) /(d)

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Assertion :Electric potential on the surface of a charged sphere of radius R is V. Then electric field at a distance r=R2 from centre is V2R Charge is distributed uniformly over the volume. Reason: From centre to surface, electric field varies linearly with r. Here, r is distance from centre.