Question 370: Electrostatics & Capacitance

Question

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu $$C charge, its radius will be :
[ Take : $${1 \over {4\,\pi { \in _0}}} = $$ 9 $$ 	imes $$ 10
9
N $$-$$ m
2
/C
2
]

Accepted Answer

Energy of sphere = $${{{Q^2}} \over {2C}}$$
$$	herefore\,\,\,$$ $${{16 	imes {{10}^{ - 12}}} \over {2C}}$$ = 4.5
$$ \Rightarrow $$$$\,\,\,$$ C = $${{16 	imes {{10}^{ - 12}}} \over 9}$$
We know capacity of spherical conductor,
C = 4$$\pi $$$$\varepsilon $$
0
R
$$	herefore\,\,\,$$ 4$$\pi $$$$\varepsilon $$
0
R = $${{16 	imes {{10}^{ - 12}}} \over 9}$$
$$ \Rightarrow $$$$\,\,\,$$ R = $${1 \over {4\pi {\varepsilon _0}}} 	imes {{16 	imes {{10}^{ - 12}}} \over 9}$$
= 9 $$ 	imes $$ 10
9
$$ 	imes $$ $${{16 	imes {{10}^{ - 12}}} \over 9}$$
= 16 mm

Answer

20 mm

Answer

32 mm

Answer

28 mm

Answer

16 mm

Electrostatics & Capacitance

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $\mu C charge, its radius will be : [ Take : {1 \over {4\,\pi { \in _0}}} = 9 \times 10 9 N -$ m 2 /C 2 ]

Choose the correct answer: