- #1
Pushpam Singh
- 6
- 0
Please explain the relation between electric potential energy and electric field in detail.
Relation between electric potential energy and electric field
- Context: Undergrad
- Thread starter Pushpam Singh
- Start date
Click For Summary
SUMMARY
The relationship between electric potential energy and electric field is defined by the equation E = -∇V, where E represents the electric field and V denotes the electric potential. This relationship arises from the fact that the electric field at a point is equal to the negative gradient of the electric potential in that direction. The path independence of the line integral allows for the expression V(r) = - ∫ E . dl, reinforcing the connection between these two concepts. The choice of reference point in defining electric potential is arbitrary, meaning different potentials can yield the same electric field.
PREREQUISITES- Understanding of vector calculus, particularly gradients
- Familiarity with electric field concepts and notation
- Knowledge of line integrals in physics
- Basic principles of electrostatics and electric potential
- Study vector calculus applications in physics, focusing on gradients
- Explore electrostatics further, particularly the concept of electric potential
- Learn about line integrals and their significance in physics
- Investigate the implications of reference points in electric potential definitions
Students of physics, electrical engineers, and anyone interested in understanding the fundamental principles of electric fields and potential energy.
- #2
d.3vil
- 11
- 0
component of the electric field at
a given point in space is equal to minus the local gradient of the electric potential in that direction...
a given point in space is equal to minus the local gradient of the electric potential in that direction...
- #3
tannerbk
- 41
- 0
Because ∇ x E = 0, it is possible to write the electric field as a gradient of some scalar. This is true for any vector whose line integral around a close loop is 0 (path indepdendence). Because the line integral is path indepdendent we define V(r) = - ∫ E . dl . It is then easy to derive E = -∇V. I think these two equations provide the best insight into the relation between the electric field and the electric potential. Remember that in the definition of the electric potential there is a choice of reference point that is arbitrary. Thus any two V's differing only in reference point correspond to the same E.
- #4
mfb
Mentor
- 37,405
- 14,241
Please do not ask questions like that, see https://www.physicsforums.com/blog.php?b=3588 for details.
Last edited by a moderator:
Similar threads
Undergrad
Electric Potential in circuit
- · Replies 3 ·
- · Replies 21 ·
- · Replies 3 ·
- · Replies 9 ·
- · Replies 10 ·
- · Replies 7 ·
- · Replies 4 ·
- · Replies 6 ·
- · Replies 7 ·
- · Replies 11 ·