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

A charge q1 = +5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -2.00 nC is placed on the positive x-axis at x = 4.00 cm. (a) If a third charge q3 = +6.00 nC is now placed at the point x = 4.00 cm, y = 3.00 cm, find the x- and y-components of the total force exerted on this charge by the other two. (b) Find the magnitude and direction of this force.

Short Answer

Expert verified

(a) The x and y components of the total force exerted on q3are 3×105Nand respectively 6.5×105N.

(b) The magnitude of this force is 7.15×109Nand the direction is 245°from +x axis.

Step by step solution

01

Orientation of charges

The charges are aligned as given in the figure:

According to superposition principle:

Fx=F21F31cosθFy=F13sinθ

02

Components of force

x direction of force is given by

Fx=kq1q2r12+kq1q3r22×xr2=9×109×5×109×2×109(0.04)29×109×5×109×6×109×0.04(0.04)2+(0.03)23/2=3×105N

y direction of force component is given by:

Fy=kq1q3r22×yr2=9×109×5×109×6×109×0.03(0.04)2+(0.03)23/2=6.5×105N

Therefore, the x and y components of the total force exerted on q3are -3×10-5Nand 6.5×105Nrespectively.

03

Magnitude and direction of force

Magnitude of f is given by

F=Fx2+Fy2=3×1052+6.5×1052=7.15×109N

The angle is given by

α=arctan6.53=65

But is in 4th quadrant so add 180

α=65+180=245

Therefore, the magnitude of this force is 7.15×10-9Nand the direction is 245°from +x axis.

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

A battery-powered global positioning system (GPS) receiver operating 9.0 V on draws a current of 0.13 A. How much electrical energy does it consume during 30 minutes?

(See Discussion Question Q25.14.) Will a light bulb glow more brightly when it is connected to a battery as shown in Fig. Q25.16a, in which an ideal ammeter is placed in the circuit, or when it is connected as shown in Fig. 25.16b, in which an ideal voltmeter V is placed in the circuit? Explain your reasoning.

The definition of resistivity (ρ=EJ) implies that an electrical field exist inside a conductor. Yet we saw that in chapter 21 there can be no electrostatic electric field inside a conductor. Is there can be contradiction here? Explain.

A typical small flashlight contains two batteries, each having an emf of1.5V, connected in series with a bulb having resistance17Ω. (a) If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b) If the batteries last for1.5hwhat is the total energy delivered to the bulb? (c) The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes, because this changes the temperature of the filament and hence the resistivity of the filament wire.)

Which of the graphs in Fig. Q25.12 best illustrates the current I in a real resistor as a function of the potential difference V across it? 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