Given charge of uniform density. What is the electrical potential @?

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SUMMARY

The electrical potential at the center of a circle with a uniform charge density of 4.50 nC/m and radius R is calculated to be 254 V. The formula used is V = kQ/r, where k is the Coulomb's constant (8.99 x 10^9 Nm²/C²). The total charge Q is derived from the linear charge density multiplied by the circumference of the circle (Q = 4.50 nC/m * 2πR). This calculation confirms that the potential is relative to zero at infinity.

PREREQUISITES
  • Understanding of electric potential and Coulomb's law
  • Familiarity with the concept of charge density
  • Knowledge of the formula for calculating potential (V = kQ/r)
  • Basic geometry related to circles (circumference calculation)
NEXT STEPS
  • Study the derivation of electric potential from continuous charge distributions
  • Learn about the implications of charge density on electric fields
  • Explore the relationship between electric potential and electric field strength
  • Investigate the effects of varying charge densities on potential calculations
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Students in physics, electrical engineering majors, and anyone interested in understanding electrostatics and electric potential calculations.

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Homework Statement


Charge of uniform density 4.50nC/m is distributed along the circle of radius R. What is the electrical potential (relative to zero at infinity) at the centre of the circle?

Answer: 254V

Homework Equations


electric potential: V=kQ/r

The Attempt at a Solution


Because the charge of uniform density is 4.50 x 10^-9 C/m
I would assumed that would equal to Q/r, and all I need to do is multiply it by k, 8.99 x 10^9Nm^2/c^2.

V= (8.99 x 10^9)(4.50 x 10^-9) = 40.455V

Of course this is incorrect, tried searching it up on google, but failed. :(
 
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If it's 4.50nC/m, what's the total charge, Q?
 
OHH! haha thanks i got it now :)

4.50nC/m * 2pi * k = 254.5V
 

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