a) What is the electric flux ?3 through the annular ring, surface 3? (Express your answer in terms of C, r1, r2, and any constants.)
b) What is the electric flux ?1 through surface 1? (Express ?1 in terms of C, r1, r2, and any needed constants.)
c) What is the electric flux ?2 passing outward through surface 2? (Express ?2 in terms of r1, r2, C, and any constants or other known quantities.)
The concept used to solve this problem is electric flux.
Initially, calculate the electric flux through the angular ring, surface 3. After that calculate the electric flux through the angular ring, surface 1. Finally, calculate the electric flux through the angular ring, surface 1.
The electric flux is defined as the measure of the electric field lines passing through the given area. More the field lines passing through the surface more will be the surface area and vice-versa.
Mathematically, the electric flux is defined as the dot product of the electric field with the component of area perpendicular to the field.
The expression of the electric flux () associated with the area element dA is given as follows:
Here, E is the electric field, A is the area and is the angle between the electric field and area element.
The electric field at position r due to point charge q is given as follows:
Here, C is the constant proportional to charge.
(a)
The angle between the electric field and the area related to surface 3 is .
The electric flux through the surface 3 is given as follows:
Substitute for in the expression .
(b)
The angle between the electric field and the area related to surface 1 is .
The electric flux through the surface 1 is given as follows:
Substitute for in the expression .
The electric field for surface 1 is given as follows:
The area element for surface 1 is given as follows:
Substitute for and for in the expression .
(c)
The angle between the electric field and the area related to surface 2 is .
The electric flux through the surface 2 is given as follows:
Substitute for in the expression .
The electric field for surface 2 is given as follows:
The area element for surface 2 is given as follows:
Substitute for and for in the expression .
Ans: Part a
Part a
AnswerThe electric flux through the surface 3 is 0.
Part bThe electric flux through the surface 1 is .
Part cThe electric flux through the surface 2 is .
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