Concept explainers
The electric field at point1 and point 2.
The electric field at point1 is
The electric field at point2 is
Given:
A sphere of radius R and surface charge density
A cavity inside the sphere of radius
Formula Used:
Gauss’s theorem
E is the electric field.
Q is the charge of the spere
Calculations:
The electric field by the sphere with cavity can be calculated as two uniform spheres of equal positive and negative charge densities.
Resultant electric field is
Substituting the values
Electric field due to negative charge density using gauss theorem
Relating
Substituting values
Substituting in the equations
Calculating the electric field by the charge Q in the cavity
Resultant electric field
At point 1
At point 2
Conclusion:
The electric field at point1 is
The electric field at point2 is
Answer to Problem 85P
The electric field at point1 is
The electric field at point2 is
Explanation of Solution
Given:
A sphere of radius R and surface charge density
A cavity inside the sphere of radius
Formula Used:
Gauss’s theorem
E is the electric field.
Q is the charge of the spere
Calculations:
The electric field by the sphere with cavity can be calculated as two uniform spheres of equal positive and negative charge densities.
Resultant electric field is
Substituting the values
Electric field due to negative charge density using gauss theorem
Relating
Substituting values
Substituting in the equations
Calculating the electric field by the charge Q in the cavity
Resultant electric field
At point 1
At point 2
Conclusion:
The electric field at point1 is
The electric field at point2 is
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