Concept explainers
Review. In fair weather, the electric field in the air at a particular location immediately above the Earth's surface is 120 N/C directed downward, (a) What is the surface charge density on the ground? Is it positive or negative? (b) Imagine the surface charge density is uniform over the planet. What then is the charge of the whole surface of the Earth? (c) What is the Earth’s electric potential due to this charge? (d) What is the difference in potential between the head and the feet of a person 1.75 m tall? (Ignore any charges in the atmosphere.) (e) Imagine the Moon, with 27.3% of the radius of the Earth, had a charge 27.3% as large, with the same sign. Find the electric force the Earth would then exert on the Moon, (f) State how the answer to part (e) compares with the gravitational force the Earth exerts on the Moon.
(a)
The surface charge density on the ground.
Answer to Problem 25.54AP
The surface charge density on the ground is
Explanation of Solution
Given info: The electric field above the earth’s surface is
Write the expression for the surface charge density.
Here,
The value of
Substitute
The direction of the electric field is downwards, so the direction of the surface charge density is negative.
Conclusion:
Therefore, the surface charge density on the ground is
(b)
The charge of whole earth.
Answer to Problem 25.54AP
The charge of whole earth is
Explanation of Solution
Given info: The electric field above the earth’s surface is
From part (a) the surface charge density on the ground is
The radius of the earth is
The area of the earth is expressed as,
Here,
Substitute
Thus, the area of the earth is
Write the expression for the charge of whole the earth.
Here,
Substitute
Conclusion:
Therefore, the charge of whole earth is
(c)
The electric potential of earth.
Answer to Problem 25.54AP
The electric potential of earth is
Explanation of Solution
Given info: The electric field above the earth’s surface is
From part (b) the charge of the earth is
Write the expression for the electric potential of earth.
Here,
The value of
Substitute
Conclusion:
Therefore, the electric potential of earth is
(d)
The electric potential difference between the head and feet of a
Answer to Problem 25.54AP
The electric potential difference between the head and feet of a
Explanation of Solution
Given info: The electric field above the earth’s surface is
Write the expression for the electric potential difference between the head and feet of a person.
Here,
Substitute
Conclusion:
Therefore, the electric potential difference between the head and feet of a
(e)
The electric force between the earth and moon.
Answer to Problem 25.54AP
The electric force between the earth and moon is
Explanation of Solution
Given info: The electric field above the earth’s surface is
The distance between moon and earth is
From part (b) the charge of earth is
The charge of moon is given by,
Thus, the value of
Write the expression for the electric force between moon and earth.
Here,
Substitute
Conclusion:
Therefore, the electric force between the earth and moon is
(f)
The comparison of the gravitation force and the electric force
Answer to Problem 25.54AP
The gravitation force is
Explanation of Solution
Given info: The electric field above the earth’s surface is
The mass of earth is
From part (e) the electric force between the earth and moon is
Write the expression for the gravitational force between moon and earth.
Here,
The value of
Substitute
Thus, the value of
Divide
Substitute
The gravitation force is
Conclusion:
Therefore, the gravitation force is
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Chapter 25 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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