• 103 selections in JEE Advanced • Student : Teacher Ratio is 12:1 • Golden Opportunity for students to be trained by IITians • Full Course Curriculum covering whole syllabus • All India Test Series Included • Regular Doubt Removal Sessions • Well Structured Time Table
Attend Free Demo Class Now
Name
 
Contact Number
   
Email ID
   
Class
 
City
 
   
IITians at your home
ISO 9001:2008 Certified
India's No. 1 Online Academy
 
Contact our Toll Free Nos
  • India Toll Free : 1-800-3070-0017
  • Bahrain (National) : 973-16198627
  • Indonesia Toll Free : 1-803-015-204-5864
  • Singapore (National) : 65-31586005
  • USA/Canada Toll Free : 1-888-442-3128
  • Others : +91-9899713975
 
operations_kei
09718199348
Contact Us More
Electric Potential and Potential Energy due to Point Charges

Consider an isolated positive point charge q. Recall that such a charge produces an electric field that is directed radially outward from the charge. To find the electric potential at a point located a distance r from the charge, we begin with the general expression for potential difference: general expression for potential difference electric potential due to point charges where A and B are the two arbitrary points shown in Figure 25.6. At any field point, the electric field due to the point charge is E = keq/r2 (Eq. 23.4), where is a unit vector directed from the charge toward the field point. The quantity E.ds can be expressed as electric potential point charges Because the magnitude of is 1, the dot product r̂.ds = ds cosθ, where θ is the angle between r̂. and ds. Furthermore, ds cos θ is the projection of ds onto r ; thus, ds cos θ = dr. That is, any displacement ds along the path from point A to point B produces a change dr in the magnitude of r, the radial distance to the charge creating the field. Making these substitutions, we find that E.ds = ( keq/r2 )dr; hence, the expression for the potential difference becomes electric potential due to point charges The integral of E.ds is independent of the path between points A and B - as it must be because the electric field of a point charge is conservative. Furthermore, Equation 25.10 expresses the important result that the potential difference between any two points A and B in a field created by a point charge depends only on the radial coordinates rA and rB . It is customary to choose the reference of electric potential to be zero at rA = ∞. With this reference, the electric potential created by a point charge at any distance r from the charge is electric potential created by a point charge Electric potential is graphed in Figure 25.7 as a function of r, the radial distance from a positive charge in the xy plane. Consider the following analogy to gravitational potential: Imagine trying to roll a marble toward the top of a hill shaped like Figure 25.7a. The gravitational force experienced by the marble is analogous to the repulsive force experienced by a positively charged object as it approaches another positively charged object. Similarly, the electric potential graph of the region surrounding a negative charge is analogous to a “hole” with respect to any approaching positively charged objects. A charged object must be infinitely distant from another charge before the surface is “flat” and has an electric potential of zero. electric potential created by a point charge We obtain the electric potential resulting from two or more point charges by applying the superposition principle. That is, the total electric potential at some point P due to several point charges is the sum of the potentials due to the individual charges. For a group of point charges, we can write the total electric potential at P in the form electric potential created by a point charge where the potential is again taken to be zero at infinity and ri is the distance from the point P to the charge qi . Note that the sum in Equation 25.12 is an algebraic sum of scalars rather than a vector sum (which we use to calculate the electric field of a group of charges). Thus, it is often much easier to evaluate V than to evaluate E. The electric potential around a dipole is illustrated in Figure 25.8.

We now consider the potential energy of a system of two charged particles. If V1 is the electric potential at a point P due to charge q1 , then the work an external agent must do to bring a second charge q2 from infinity to P without acceleration is q2V1. By definition, this work equals the potential energy U of the two-particle system when the particles are separated by a distance r12 (Fig. 25.9). Therefore, we can express the potential energy as potential energy created by a point charge Note that if the charges are of the same sign, U is positive. This is consistent with the fact that positive work must be done by an external agent on the system to bring the two charges near one another (because like charges repel). If the charges are of opposite sign, U is negative; this means that negative work must be done against the attractive force between the unlike charges for them to be brought near each other.
If more than two charged particles are in the system, we can obtain the total potential energy by calculating U for every pair of charges and summing the terms algebraically. As an example, the total potential energy of the system of three charges shown in Figure 25.10 is total potential energy created by three point charges Physically, we can interpret this as follows: Imagine that q1 is fixed at the position shown in Figure 25.10 but that q2 and q3 are at infinity. The work an external agent must do to bring q2 from infinity to its position near q1 is keq1q2/ r12 which is the first term in Equation 25.14. The last two terms represent the work required to bring q3 from infinity to its position near q1 and q2 . (The result is independent of the order in which the charges are transported.) potential energy created by two point charges potential energy created by three point charges electric potential in plane containing a dipole

electric potential due to two point charges
Do you like this Topic?
Share it on
       
       
  • Online Classroom Program

    • IITians @ Your Home, Attend Classes directly from Home
    • Two way interaction between Teacher and Students
    • Zero Travel Time or Cost involved, No Hidden Charges
    • Small Batch Sizes, Maximum of 8-10 Students
    • Golden Opportunity to be trained by IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE Online Classes
  • 1 on 1 Online Class

    • IITians @ your Home for 1 on 1 Class
    • Two way Communication between Teacher and Student
    • Special Doubt Removal & Problem solving Sessions
    • Customize the Course as per your desire - Duration, Timing, Faculty etc
    • All faculties are IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE 1 on 1 Online Classes
  • Correspondence Course Details

    • 600 Hours of Recorded Lectures by IITians and NITians
    • Best Study Material comprising all Concepts and Tricks
    • 10000+ Solved Question Bank + 250 Hours of Video Solutions
    • Complete NCERT solutions + 150 Hours of NCERT Video Solutions
    • Last 30 years JEE chapterwise video solutions
    • 100% Original Material prepared by JEE Experts
    Register for Free Now IIT JEE Correspondence Courses
  • AITS for JEE Main and JEE Advanced

    Register for Free Now JEE Test Series
X

Welcome to Kshitij Education India

Our Guarantee:

We're so sure you'll have the time of your life with us, we back our courses with a 100% Satisfaction Guarantee.

If for any reason you aren't 100% satisfied with your classes in first 7 days, just let us know and we'll refund your fees. No questions asked.

And based on your feedback, we will take the necessary steps to ensure we never repeat any mistakes as such.

Live Chat