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Chapter 23: Q. 65 (page 657)

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these

a. Write a realistic problem for which this is the correct equation(s).

b. Finish the solution of the problem

η2ε0[1-zz2+R2]=12η2ε0

Short Answer

Expert verified

(a) A disc with a radius of Rand a charge of Qthat is uniformly distributed. Discover an equation for the strength of the electric field at a point Pon the axis at a distance zfrom the center.

(b) The solution isz=R3

Step by step solution

01

Given information and formula used

Given :

η2ε0[1-zz2+R2]=12η2ε0

Theory used :

The electric field due to a uniformly charged disc at a point very distant from the surface of the disc is given by:

E=σ2ε0

(σ is the surface charge density on the disc)

02

Writing a realistic problem and finding the solution of the problem 

(a) Realistic problem :

Given a disc with a radius of Rand a charge of Qthat is uniformly distributed. Discover an equation for the strength of the electric field at a point Pon the axis at a distance zfrom the center. If

η2ε0[1-zz2+R2]=12η2ε0

(b) Solution :

From the previous expression, finding the value of z :

η2ε0[1-zz2+R2]=12η2ε0⇒1-zz2+R2=12⇒z2z2+R2=14⇒z2+R2=4z2⇒z=R3

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Most popular questions from this chapter

An infinite plane of charge with surface charge density 3.2μC/m2has a 20-cm-diameter circular hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12cm?

Hint: Can you create this charge distribution as a superposition of charge distributions for which you know the electric field?

You have a summer intern position with a company that designs and builds nanomachines. An engineer with the company is designing a microscopic oscillator to help keep time, and you’ve been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal ring. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the ring.

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c. Evaluate the oscillation frequency for an electron at the center of a 2.0μmdiameter ring charged to 1.0×10-13C.

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