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Question
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 N/C and points radially inward, what is the net charge on the sphere?
Solution
Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation,
`"E" = 1/(4piε_0r^2)`
Where,
q = Net charge = 1.5 × 103 N/C
d = Distance from the centre = 20 cm = 0.2 m
ε0 = Permittivity of free space
And, `1/(4piε_0)` = 9 × 109 N m2 C−2
∴ `"q" = "E"(4piε_0)"d"^2`
= `(1.5xx10^3xx(0.2)^2)/(9xx10^9)`
= 6.67 × 10-9 C
Charge is negative, or anti-static, because the electric field is inward-pointing.
q = - 6.67 nC.
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