Q. 214.1( 40 Votes )
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?
Radius of charged sphere, r = 10 cm
Electric field, 20 cm away from centre of sphere, E = 1.5 × 103 NC-1
We know that, electric field intensity at a point P, located at a distance R, due to net charge q is given by,
Now plugging the values of q and R in equation (1)
q = 4 × π × ε0 × R2 × E
⇒ q = 4 × 3.14 × 8.85 × 10-12N-1m-2C-2 × (0.2m)2 × 1.5 × 103C
⇒ q = 6.67 × 10-9C
The net charge on the sphere is -6.67 × 10-9C. Since the electric field points radially inwards, we can infer that charges on sphere are negative.
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Five charges, q each are placed at the corners of a regular pentagon of side ‘a’ (Fig. 1.12).
(a) (i) What will be the electric field at O, the center of the pentagon?
(ii) What will be the electric field at O if the charge from one of the corners (say A) is removed?
(iii) What will be the electric field at O if the charge q at A is replaced by –q?
(b) How would your answer to (a) be affected if pentagon is replaced by n-sided regular polygon with charge q at each of its corners?
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(i) What is the net electric field on the Cl atom due to eight Cs atoms?
(ii) Suppose that the Cs atom at the corner A is missing. What is the net force now on the Cl atom due to seven remaining Cs atoms?
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