Concept explainers
(a)
The surface charge density on the ground, and whether the surface charge density is positive or negative.
(a)
Answer to Problem 62P
The surface charge density on the ground is
Explanation of Solution
Consider the earth’s surface as a charged
Write the expression for electric field due to charged conducting plane.
Here,
Rearrange equation (I), to find
Conclusion:
Substitute
The electric field inside the conducting earth is zero, the electric field is in downward direction. thus the earth is negatively charged.
Therefore, the surface charge density on the ground is
(b)
The charge of total surface of earth.
(b)
Answer to Problem 62P
The charge of total surface of earth is
Explanation of Solution
Write the expression for charge in terms of surface charge density.
Here,
Due to spherical symmetry of the earth, the surface area is
Apply the condition in the above equation (III), to find
Conclusion:
Substitute
Therefore, the charge of total surface of earth is
(c)
The electric force on the moon exerted by the earth.
(c)
Answer to Problem 62P
The electric force on the moon exerted by the earth is
Explanation of Solution
Given that the charge on the moon is
Write the expression electrostatic force.
Here,
Conclusion:
Substitute
Therefore, the electric force on the moon exerted by the earth is
(d)
Compare the result in subpart (c) with gravitational force on moon due to the earth.
(d)
Answer to Problem 62P
The gravitational force is
Explanation of Solution
From subpart (c), the electric force on the moon exerted by the earth is
Write the expression for gravitational force.
Here,
Conclusion:
Substitute
Divide equation (VII) by (VIII), to find
Rearrange the above equation to find
Therefore, the gravitational force is
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Chapter 19 Solutions
Principles of Physics
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