Calculating Electric Field for Charged Ring on x,y Axes

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SUMMARY

The discussion centers on calculating the electric field generated by a charged ring positioned on the x,y axes, where the top half has a charge density of -λ and the bottom half +λ. The electric field at the center is given by E = (λy)/(2πεR), with ε representing the permittivity of free space. Participants emphasize the importance of finding the electric potential first, as it simplifies the process of deriving the electric field through partial differentiation. A critical point raised is the inconsistency in the initial expression, which suggests that the electric field increases with distance from the ring, contradicting established physical principles.

PREREQUISITES
  • Understanding of electric fields and potentials in electrostatics
  • Familiarity with charge density concepts and their implications
  • Knowledge of calculus, specifically partial derivatives
  • Basic principles of electromagnetism, including the role of permittivity (ε)
NEXT STEPS
  • Study the derivation of electric potential for charged distributions
  • Learn about the relationship between electric field and electric potential
  • Explore the concept of charge density and its effects on electric fields
  • Investigate the implications of electric field behavior at varying distances from charged objects
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism, as well as anyone involved in solving problems related to electric fields and potentials in charged systems.

mickry
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Homework Statement



I have the field at the center of a charged ring on the x,y axes (top half has charge density of -lambda, bottom is +lambda lambda=la) to be
E=(lay^)/(2pi epsR) (eps=epsilon) i can't find the potential for this, R=radius,
Can anyone help?

Homework Equations





The Attempt at a Solution

 
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Normally, it's easier to find the potential first, as it is a scalar, and then take the partial derivative with respect to the distance variable to determine the E-Field.

In this case, your expression doesn't make sense.

<br /> E = \frac{\lambda y}{2 \pi \epsilon_0 R}<br />

Are you sure that's correct? Because that implies that as you get further away from the ring, the e-field increases, which doesn't make sense.
 

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