Concept explainers
Review. Two insulating spheres have radii r1 and r2, masses m1 and m2, and uniformly distributed charges −q1 and q2. They are released from rest when their centers are separated by a distance d. (a) How fast is each moving when they collide? (b) What If? It the spheres were conductors, would their speeds be greater or less than those calculated in part (a)? Explain.
(a)
Answer to Problem 18P
Explanation of Solution
Given info: The radius of sphere 1 is
Consider the diagram of two insulating sphere having charge
Figure (1)
Write the expression to calculate the electric potential energy before collide,
Here,
Write the expression to calculate the potential energy after collide,
Here,
Add equation (1) and equation (2).
Write the equation of kinetic energy stored in charged sphere after collide, if velocity of charged sphere 1 is
Here,
From the law of conservation, both charged mass gets kinetic energy on diminishing of electric potential energy.
Then for equilibrium condition both energies will be same that is,
The negative sign shows that there is decrease in electric potential energy.
Substitute
Write the equation for conservation of momentum for final velocities of charged spheres.
Substitute
Substitute
Conclusion:
Therefore, the velocity of sphere 1 after collide is
(b)
Answer to Problem 18P
Explanation of Solution
Given info: The radius of sphere 1 is
Due to polarization, the most of the positive charge of one sphere at the centre and most of the negative charge at the centre of other sphere will attracts each other due to which their average centre distance will be less then geometric centre distance. Hence potential energy will be less and kinetic energy will be more for conducting sphere, hence due to more kinetic energy velocities of conducting spheres after collide will be more.
Conclusion:
Therefore, the velocities of conducting sphere after collide will be more than velocities of insulating sphere after collide due to effect polarization.
Want to see more full solutions like this?
Chapter 24 Solutions
Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
- 2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward2-3. Consider the situation of the reflection of a pulse at the interface of two string described in the previous problem. In addition to the net disturbances being equal at the junction, the slope of the net disturbances must also be equal at the junction at all times. Given that p1 = 4.0 g/m, H2 = 9.0 g/m and Aj = 0.50 cm find 2. A, (Answer: -0.10 cm) and 3. Ay. (Answer: 0.40 cm)please I need to show all work step by step problems 2 and 3arrow_forwardFrom number 2 and 3 I just want to show all problems step by step please do not short cut look for formulaarrow_forward
- Look at the answer and please show all work step by steparrow_forward3. As a woman, who's eyes are h = 1.5 m above the ground, looks down the road sees a tree with height H = 9.0 m. Below the tree is what appears to be a reflection of the tree. The observation of this apparent reflection gives the illusion of water on the roadway. This effect is commonly called a mirage. Use the results of questions 1 and 2 and the principle of ray reversibility to analyze the diagram below. Assume that light leaving the top of the tree bends toward the horizontal until it just grazes ground level. After that, the ray bends upward eventually reaching the woman's eyes. The woman interprets this incoming light as if it came from an image of the tree. Determine the size, H', of the image. (Answer 8.8 m) please show all work step by steparrow_forwardNo chatgpt pls will upvotearrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegeCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning