An electric field converges at the origin whose magnitude is given by the expression $E = 100 r \frac{N}{C}$ , where r is the distance measured from the origin.

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total charge contained in a spherical volume of radius 3 cm with its centre at origin has magnitude $3 \times 10^{- 9} C$ .

total charge contained at any spherical volume, irrespective of the location of its centre, is negative.

total charge contained in any spherical volume with its centre at origin is negative.

total charge contained in a spherical volume of radius 3 cm with its centre at origin has magnitude $3 \times 10^{- 13} C$ .

answer is A, B, C.

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Detailed Solution

In the case of converging electric field the charge should be negative.

$\Rightarrow E = \frac{1}{4 π ϵ_{0}} \frac{q}{r^{2}} = - 100 r \Rightarrow q = - 400 {πϵ}_{0} r^{3}$

So the charge contained at any spherical volume irrespective of the location of its centre is negative.(Negative charge is distributed over space)

$For circle of radius 3 cm with centre at origin . \Rightarrow 9 \times 10^{9} \frac{q}{9 \times 10^{- 4}} = - 100 \times 3 \times 10^{- 2}$

$\Rightarrow q = - 3 \times 10^{- 13} C$

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