Concept explainers
(a)
The electric field between the two parallel metal plates.
(a)
Explanation of Solution
Given:
Area of the two plates is
Separation between the plates is
The amount of charge that is transfer from left plate to the right is
Formula used:
Draw a diagram to show the surface charge density of the two metal parallel plates 1 and 2.
Write the expression of electric field due to a plane surface.
Here,
Write the expression for the surface charge density due to the plane 1.
Here,
Write the expression for the surface charge density due to the plane 2.
Here,
Calculation:
The electric field at a distance
Here,
Substitute
Charge of the plates is equal but opposite sue to the transfer of charges from one plate to another.
Substitute
Substitute
Here,
Substitute
Conclusion:
Thus, the electric field is
(b)
The electric field between the two parallel metal plates.
(b)
Explanation of Solution
Given:
Area of the two plates is
Separation between the plates is
The amount of charge that is transfer from left plate to the right is
Formula used:
Write the expression of electric field due to a plane surface.
Here,
Write the expression for the surface charge density due to the plane 1.
Here,
Write the expression for the surface charge density due to the plane 2.
Here,
Calculation:
The electric field at a distance
Here,
Substitute
Charge of the plates is equal but opposite sue to the transfer of charges from one plate to another.
Substitute
Substitute
Here,
Substitute
Conclusion:
Thus, the electric field is
(c)
The electric field to the left of the left plate.
(c)
Explanation of Solution
Given:
Area of the two plates is
Separation between the plates is
The amount of charge that is transfer from left plate to the right is
Formula used:
Write the expression of electric field due to a plane surface.
Here,
Write the expression for the surface charge density due to the plane 1.
Here,
Write the expression for the surface charge density due to the plane 2.
Here,
Calculation:
The electric field to the left from the plate on left.
Here,
Substitute
Charge of the plates is equal but opposite sue to the transfer of charges from one plate to another.
Substitute
Conclusion:
Thus, the electric field is
(d)
The electric field to the right of the right plate.
(d)
Explanation of Solution
Given:
Area of the two plates is
Separation between the plates is
The amount of charge that is transfer from left plate to the right is
Formula used:
Write the expression of electric field due to a plane surface.
Here,
Write the expression for the surface charge density due to the plane 1.
Here,
Write the expression for the surface charge density due to the plane 2.
Here,
Calculation:
The electric field to the right from the plate on right.
Here,
Substitute
Charge of the plates is equal but opposite sue to the transfer of charges from one plate to another.
Substitute
Conclusion:
Thus, the electric field is
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Chapter 22 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
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