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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]=12η2ε01-zz2+R2=12z2z2+R2=14z2+R2=4z2z=R3

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Most popular questions from this chapter

An electric field can induce an electric dipole in a neutral atom or molecule by pushing the positive and negative charges in opposite directions. The dipole moment of an induced dipole is directly proportional to the electric field. That is, p=αE, where αis called the polarizability of the molecule. A bigger field stretches the molecule farther and causes a larger dipole moment.

a. What are the units of α?

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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

(9.0×109Nm2/C2)2(2.0×10-7C/m)r=25000N/C

Two circular disks spaced0.50mmapart form a parallel-plate capacitor. Transferring3.0×109electrons from one disk to the other causes the electric field strength to be2.0×105N/C. What are the diameters of the disks?

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