Guest

The electric field in aregion is radially outward and at a point is given by E=250r V/m [where r is the distance of the point from the origin] .Calculate the charge contained in a sphere of radius 20cm, centered at the origin.

The electric field in aregion is radially outward and at a point is given by E=250r  V/m [where r is the distance of the point from the origin] .Calculate the charge contained in a sphere of radius 20cm, centered at the origin.

Grade:12th Pass

2 Answers

KJ S
18 Points
12 years ago

As we know the flux through the sphere is not zero so we apply gauss law.
E.dS=Q/epsilon. As E varies integrate with limits from 0 to 0.2 m.
250rd(4∏r2)=Q/epsilon
250r x 4 x ∏ x 2 x rd(r) = Q/episilon
now integrating we get
200∏R3/3 x epsilon =Q
Plimits to get final Ans.

Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Hello student
As per Gauss law, Electric flux is given by
∫E.dA = E.A = qin0
now surface area for spherical surface, A = 4πR
For a sphere of radius, R = 20 cm, A = 4π(0.2)2
E= 250r V/m = 250 x 0.2 = 50 V/m
 
Hence, qin= E.A = 50 x  4π(0.2)2
                                       = 200 x 3.14 x 0.04 = 25.12
Hence, enclosed charge, qin. = 25.12 x εC
                                               = 25.12 x 8.854 x 10-12 
                                               = 2.224 x 10-10 C
 
Hope it helps.
Regards,
Kushagra

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free