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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.
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Chapter 24 Solutions
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