A solid non-conducting sphere of radius R having variable volume charge density where is the distance from centre. If electric field at distance from the centre of charged sphere is . Value of will be

Question

A solid non-conducting sphere of radius R having variable volume charge density $d = \frac{A r}{R}$ where $r$ is the distance from centre. If electric field at distance $\frac{R}{2}$ from the centre of charged sphere is $E = \frac{2 R}{ε_{0}} N/C$ . Value of $\frac{A}{16}$ will be

Smart Achievers · Accepted Answer

(1)

$According to Gauss law$

$\oint \vec{E} \cdot d \vec{s} = \frac{q_{i n}}{ε_{0}}$

$q_{i n} = \int_{0}^{R / 2} d \cdot 4 π r^{2} d r$

$Solving \frac{A}{16} = 2$

Solution

Q.
A solid non-conducting sphere of radius R having variable volume charge density $d = \frac{A r}{R}$ where $r$ is the distance from centre. If electric field at distance $\frac{R}{2}$ from the centre of charged sphere is $E = \frac{2 R}{ε_{0}} N/C$ . Value of $\frac{A}{16}$ will be

1 2

2 4

3 6

4 8

Ans.
(1)

$According to Gauss law$

$\oint \vec{E} \cdot d \vec{s} = \frac{q_{i n}}{ε_{0}}$

$q_{i n} = \int_{0}^{R / 2} d \cdot 4 π r^{2} d r$

$Solving \frac{A}{16} = 2$

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Solution

Q. A solid non-conducting sphere of radius R having variable volume charge density d=ArR where r is the distance from centre. If electric field at distance R2 from the centre of charged sphere is E=2Rε0 N/C. Value of A16 will be

1 2

2 4

3 6

4 8

Ans. (1) According to Gauss law ∮E→·ds→=qinε0 qin=∫0R/2d·4πr2 dr Solving A16=2

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Q.
A solid non-conducting sphere of radius R having variable volume charge density $d = \frac{A r}{R}$ where $r$ is the distance from centre. If electric field at distance $\frac{R}{2}$ from the centre of charged sphere is $E = \frac{2 R}{ε_{0}} N/C$ . Value of $\frac{A}{16}$ will be

Ans.
(1)

$According to Gauss law$

$\oint \vec{E} \cdot d \vec{s} = \frac{q_{i n}}{ε_{0}}$

$q_{i n} = \int_{0}^{R / 2} d \cdot 4 π r^{2} d r$

$Solving \frac{A}{16} = 2$