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How to do this ? Shouldn’t the answer be 0 since the net enclosed charge is 0 ?

How to do this ?
Shouldn’t the answer be 0 since the net enclosed charge is 0 ?
 

Question Image
Grade:12

1 Answers

Mallikarjun Maram
50 Points
6 years ago
Answer is not zero.  As the surface is not closed surface.  To solve this problem look at the picture below:
 
 
p { margin-bottom: 0.25cm; line-height: 120%; }

Let us construct a cylinder as shown in the figure, with R (radius of hemisphere) is the radius of the cylinder and 2R is its length. Now you can see that the charge q will be at the center of the cylinder.

Let

S1 = end surface of the cylinder, φ1 = flux through S1

S2 = half of the curved surface of the cylinder, φ2 = flux through S2

S = is the curved surface of the hemisphere and φ = flux through S

Since flux through the central plane is zero, by symmetry we have φ! + φ2 = q/2εo

We can also see that φ = φ2 = (q/2εo)φ1

Since the surface subtends a plane angle of 90o at the q, the corresponding solid angle can be calculated using the formula , where α is the plane angle subtended.

Thus φ1 can be calculated as

Finally the required value

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