Chapter 21: Problem 28
The earth has a net electric charge that causes a field at points near its surface equal to 150 N\(/\)C and directed in toward the center of the earth. (a) What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field? (b) What would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? Is use of the earth's electric field a feasible means of flight? Why or why not?
Short Answer
Step by step solution
Calculate Force due to Weight
Calculate Required Electric Force
Calculate Charge to Overcome Weight
Apply Newton's Third Law for Same Charges
Calculate Force Between Two Charged Individuals
Evaluation of Feasibility
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electrostatic Force
This force can be either attractive or repulsive, depending on the types of charges involved. Like charges repel each other, while opposite charges attract.
The magnitude of the electrostatic force between two point charges is determined by combining the magnitudes of the charges and the distance between them. The force is much more significant over shorter distances, but can still pack a punch even at a distance, depending on the charge magnitude. This is why understanding electrostatic forces is crucial, especially in applications like levitation or electronics.
Coulomb's Law
The law is expressed by the formula: \[ F = \frac{k \times |q_1 \times q_2|}{r^2} \] where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant \( (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \),
- \( q_1 \) and \( q_2 \) are the amounts of the charges,
- \( r \) is the distance between the centers of the two charges.
Electric Charge
Charge conservation is an important principle, indicating that the total electric charge in an isolated system remains constant regardless of changes within the system.
Objects become charged by gaining or losing electrons. When an object has more electrons than protons, it is negatively charged. When it has fewer electrons, it is positively charged. This transfer of charge is the essence of electrostatic phenomena, influencing how objects interact through electric forces.
Gravitational Force
This force is calculated using Newton's law of universal gravitation, given by:\[ F_{gravity} = \frac{G \times m_1 \times m_2}{r^2} \]where:
- \( F_{gravity} \) is the gravitational force between two masses,
- \( G \) is the gravitational constant \((6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2)\),
- \( m_1 \) and \( m_2 \) are the masses,
- \( r \) is the distance between the centers of the two masses.
Feasibility of Electromagnetic Levitation
In the outlined exercise, the charge needed for levitation is unreasonably high. Achieving a charge sufficient to counteract the gravitational pull on a human is not practical with our current technology and safety considerations.
- The required charge is difficult to obtain or sustain due to the massive electric capacitance involved.
- Generous expenses and technological limitations make everyday use of electromagnetic levitation infeasible for large objects like humans.
- Despite this, the concept has found success in specialized areas like magnetic trains and industrial applications, where controlled environments and setups are possible.