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Chapter 8: Q 13-31MP (page 467)

Question: The acceleration of an electron in the electric field of a positively charged sphere is inversely proportional to the square of the distance between the electron and the center of the sphere. Let an electron fall from rest at infinity to the sphere. What is the electron’s velocity when it reaches the surface of the sphere?

Short Answer

Expert verified

The acceleration of the electron is inversely proportional to the square of the distance between the electron and center of sphere.

Step by step solution

01

Given Information

The acceleration of the electron is inversely proportional to the square of the distance between the electron and center of sphere.

02

The acceleration of an object

The rate of change of velocity is known as acceleration. It is given by a = dv / dt

03

Speed of Electron

04

The velocity of electron

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Most popular questions from this chapter

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example 1.

y'+ytanhx=2ex

Use L32 and L11 to obtainL(t2sinat).

Solve the following sets of equations by the Laplace transform method

.y'+2z=1y0=02y-zz'=2tz0=1

Using Problems 29 and 31b, show that equation (6.24) is correct.

Several Terms on the Right-Hand Side: Principle of Superposition So far we have brushed over a question which may have occurred to you: What do we do if there are several terms on the right-hand side of the equation involving different exponentials?

In Problem 33 to 38 , solve the given differential equations by using the principle of superposition [see the solution of equation (6.29) . For example, in Problem 33 , solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus a polynomial of any degree is kept together in one bracket.

y"-5y'+6y=2ex+6x-5

In Problems 13 to 15, find a solution (or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3.

13. Problem 2
See all solutions

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