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 particle of charge Qis fixed at the origin of an x-ycoordinate system. Att=0a particle (m=0.800g,q=4.00μC) is located on the xaxis atx=20.0cm, moving with a speed of50.0m/sin the positive ydirection. For what value of Qwill the moving particle execute circular motion? (Neglect the gravitational force onthe particle.)

Short Answer

Expert verified

The value of Q for which the moving particle will execute circular motion is1.11×105C

Step by step solution

01

The given data 

At t=0a particle(m=0.800 gor0.008 g,q=4.00 μCor4×106C) is located on the x axis at, x=20.0 cmor0.2 mmoving with a speed of v=50.0 m/sin the positive y-direction

02

Understanding the concept of Coulomb’s law and centripetal force

For a moving body to exhibit circular motion, the body must have centripetal force acting on it. Hence, in this case, the centripetal force is balanced by the electrostatic force. This determines the value of Q.

Formulae:

The magnitude of the electrostatic force between any two particles,F=kq1q2r2 (i)

The centripetal force acting on a body in circular motion, role="math" localid="1661866945126" a=v2/r (ii)

03

Calculation of the value of charge, Q 

For the Coulomb force to be sufficient for circular motion at that distance (where r=0.200m) the following condition is given using equations (i) and (ii) as follows:

Qq4πε0r2=mv2r(negativesignastheforceisinward)Q=4πε0r.mv2q=(0.200m)(8.00×104kg)(50.0m/s)2(9.00×109Nm2/C2)(4×106C)=1.11×105C

Hence, the value of the charge is1.11×105 C

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

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