Question

A spherical surface surrounds a point charge q. Describe what happens to the total flux through the surface if the following happens:
(a) The charge is tripled.
*The flux is tripled.
*The flux decreases by 1/3.
*The flux remains constant.
*The flux goes to zero.

(b) The volume of the sphere is doubled.

*The flux is tripled.
*The flux decreases by 1/3.
*The flux remains constant.
*The flux goes to zero.

(c) The surface is changed to a cube.
*The flux is tripled.
*The flux decreases by 1/3.
*The flux remains constant.
*The flux goes to zero.

(d) The charged is moved to another location inside the surface.

*The flux is tripled.
*The flux decreases by 1/3.
*The flux remains constant.
*The flux goes to zero.

(e) The charge is moved outside the surface.

*The flux is tripled.
*The flux decreases by 1/3.
*The flux remains constant.
*The flux goes to zero.

Answer 1

Answer:

A. The flux tripled

B. The flux doubled

C. The flux remains constant

D. The flux remains constant

E. The flux remains constant

Explanation:

Using Gauss law, total flux = E. dA

Where Electric field, E = kQ/R2 and k = 1/4pieo where eo = permittivity of space

Area of a sphere, A = 4piR2

A. If the charge is tripled

Total flux is tripled because flux is directly proportional to the charge

B. Volume of the sphere is doubled

Volume = Area * R/3

If volume is doubled, Area increases by 6/R

So, area is doubled

Area is directly proportional to the total flux

C. The surface is a cube

The total flux does not change because all Electric field lines pass horizontally regardless of its radius

D.

The total flux doesn't change because Gauss law talks about an enclosed charged, the location of the charge is not necessary.

E.

The electric field outside the sphere os the same as the point charge. For the radius outside the sphere, a therefore r>a

So, it remains constant.