Question

# The diagram shows a sphere of radius $$R$$ that carries a charge uniformly distributed throughout its volume. The volume charge density is $$\rho$$. A Gaussian sphere of radius $$a$$ is imagined that is concentric to the charged sphere.If $$a>R$$, what is the charge enclosed in the Gaussian surface?

A
Qenc=4πρR2
B
Qenc=43πρa3
C
Qenc=4πρa2
D
Qenc=43πρR3
E
Qenc=πρa2

Solution

## The correct option is B $$Q_{enc} = \cfrac{4}{3}\pi \rho R^3$$The volume charge density is given by ,                                 $$\rho=$$charge on sphere / volume of sphere                                 $$\rho=Q/\frac{4}{3}\pi R^{3}$$or                             $$Q=\frac{4}{3}\pi \rho R^{3}$$we can see that the charge enclosed by gaussian surface is equal to $$Q$$ i.e.$$Q_{enc}=Q$$therefore   $$Q_{enc}=\frac{4}{3}\pi \rho R^{3}$$Physics

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