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

Three point charges are arranged on a line. Charge q3=+5.00nCand is at the origin. Charge q2=-3.00nCand is at x=+4.00cm. Charge q1is atx=+2.00cm . What is q1 (magnitude and sign) if the net force on q3is zero?

Short Answer

Expert verified

The magnitude and sign of q1 is +0.75nC.

Step by step solution

01

Coulomb’s law

Coulomb's law states that the magnitude F of the force exerted by two-point charges q1 and q2 separated by is directly proportional to the product of the charges(q1×q2) and inversely proportional to the square of the distance between them.

F=kq1q2r2

Here; F is the force on each point charge exerting on each other, k is the proportionality constant, r is the distance between the charges q1 and q2.

02

Magnitude and sign of q1 is

Consider the given data as below.

The charge,q2=-3.00nC=-3.00×10-9C

The charge, q3=+5.00nC=+5.00×10-9C

The force, F = 0.600 N

The distance between two point charges,

The Coulomb’s constant,k=9×109N·m2/C2

Draw the free body diagram as below.

The charge exerts a force on charge q3, the net force acting on q3 is zero.

As q3 is affected by two forces F13 and F23, thus, the net force is;

Fnet=F13+F23

Thus, the charge q1 towards the positive x-direction, which is a repulsive force between q3 and q1, so the net force is;

F13=F23kq1q3r12=kq2q3r22q1r12=q2r22q1=q2r12r22

Substitute known values ion the above equation, and you have

q1=∣3.00nCl2.00cm4.00cm2=+3.00nC4.00=+0.75nC

Hence, the magnitude and sign of q1 is +0.75nC.

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

A25.0-Ωbulb is connected across the terminals of a12.0-Vbattery having3.50Ωof internal resistance. What percentage of the power of the battery is dissipated across the internal resistance and hence is not available to the bulb?

An idealized ammeter is connected to a battery as shown in Fig.

E25.28. Find (a) the reading of the ammeter, (b) the current through the4.00Ω

resistor, (c) the terminal voltage of the battery.

Fig. E25.28.

In the circuit shown in Fig. E26.18,ε=36.V,R1=4.0Ω,R2=6.0Ω,R3=3.0Ω(a) What is the potential difference Vab between points a and b when the switch S is open and when S is closed? (b) For each resistor, calculate the current through the resistor with S open and with S closed. For each resistor, does the current increase or decrease when S is closed?

A particle with charge-5.60nCis moving in a uniform magnetic fieldrole="math" localid="1655717557369" B=-(1.25T)k^

The magnetic force on the particle is measured to berole="math" localid="1655717706597" F=-(3.40×10-7N)i^-(7.40×10-7N)j^ (a) Calculate all the components of the velocity of the particle that you can from this information. (b) Are there
components of the velocity that are not determined by the measurement of the force? Explain. (c) Calculate the scalar productv֏F. What is the angle between velocity and force?

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H-(the hydride ion, which has one proton and two electrons) to an energy of 5MeVto20MeV.This ion has a mass very close to that of a proton because the electron mass is negligible about 12000of the proton’s mass. A typical magnetic field in such cyclotrons is 1.9T..(a) What is the speed of a 5.0-MeVH-? (b) If the H-has energy 5.0MeVandB=1.9T what is the radius of this ion’s circulator orbit?

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