Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 23: 40 - Excercises And Problems (page 655)

Derive Equation 23.11for the field Edipolein the plane that bisects an electric dipole.

Short Answer

Expert verified

The Equitorial time at field point is P4πε0r3.

Step by step solution

01

Step: 1 Electric field:

The electric field radial component by

Er=rEr=rPcosθ4πε0r2Er=Pcosθ4πε0Lr3Er=2Pcosθ4πε0r3

02

Step; 2 Transverse electric field:

The component transverse of electric field by

Eθ=1rEθEθ=1rθPcosθ4πε0r2Eθ=Psinθ4πε0r3

03

Step: 3 Resultant field:

The resultant field by,

E=2Pcosθ4πε0r32+Psinθ4πε0r32E=P4πε0r34cos2θ+sin2θE=P4πε0r31+3cos2θ

04

Step; 4 Field angle:

The angle at field,

tanϕ=EθErtanϕ=Psinθ4πε0r3tanϕ=2Pcosθ4πε0r3tanϕ=12sinθcosθ.

Because of magnitude and direction in dipole,the angle on equitorial time at θ=90

Therefore,the equitorial time on field point isP4πε0r3.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Three charges are placed at the corners of the triangle in FIGURE Q23.15. The ++charge has twice the quantity of charge of the two - charges; the net charge is zero. Is the triangle in equilibrium? If so, explain why. If not, draw the equilibrium orientation.

A small object is released at point 3in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed?

a. A positive object is released from rest.

b. A neutral but polarizable object is released from rest.

c. A negative object is released from rest.

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.

a. Consider a negative charge near the center of a positively charged ring centered on the z-axis. Show that there is a restoring force on the charge if it moves along the z-axisbut stays close to the center of the ring. That is, show there’s a force that tries to keep the charge at z=0. b. Show that for small oscillations, with amplitude <<R, a particle of mass mwith charge-qundergoes simple harmonic motion with frequency f=12πqQ4πε0mR3,RandQare the radius and charge of the ring.

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

A10-cmlong thin glass rod uniformly charged to+10nCand a 10-cm-long thin plastic rod uniformly charged to-10nCare placed side by side, 4.0cmapart. What are the electric field strengthsE1toE3at distances1.0cm,2.0cm, and from the glass rod a3.0cmlong the line connecting the midpoints of the two rods?

Rank in order, from largest to smallest, the electric field strengths E1 to E5 at the five points inFIGURE Q23.11. Explain.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free