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 × 10^3 N/C and points radially inward, what is the net charge on the sphere? - Physics

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Numerical

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 × 10N/C and points radially inward, what is the net charge on the sphere?

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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" = "q"/(4piin_0"d"^2)`

Where,

q = Net charge = 1.5 × 103 N/C

d = Distance from the centre = 20 cm = 0.2 m

0 = Permittivity of free space

And, `1/(4piin_0)` = 9 × 109 N m2 C−2

∴ `"q" = "E"(4piin_0)"d"^2`

= `(1.5xx10^3xx(0.2)^2)/(9xx10^9)`

= 6.67 × 109 C

= 6.67 nC

Therefore, the net charge on the sphere is 6.67 nC.

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Chapter 1: Electric Charges and Fields - Exercise [Page 48]

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NCERT Physics Class 12
Chapter 1 Electric Charges and Fields
Exercise | Q 1.21 | Page 48
NCERT Physics Class 12
Chapter 1 Electric Charge and Fields
Exercise | Q 21 | Page 48

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