Got stuck Electric Potential due to Dipole

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SUMMARY

The discussion focuses on calculating the electric potential due to a tiny dipole with a dipole moment of 6.0×10−30 C*m at a distance of 3.6×10−9 m. For part a, the potential along the axis near the positive charge is calculated as V = 4.2 x 10−3 V using the formula V = (1/(4πE))(q/d). The user encountered difficulties in parts b and c, which involve calculating the potential at 45 degrees above the axis. Key steps include drawing a diagram, calculating distances from each charge, and applying the dipole moment in the potential equations.

PREREQUISITES
  • Understanding of electric dipole moment and its significance.
  • Familiarity with the formula for electric potential due to point charges.
  • Knowledge of trigonometric functions, particularly for angle calculations.
  • Basic principles of electrostatics, including the concept of permittivity of free space.
NEXT STEPS
  • Learn how to calculate electric potential due to dipoles in different orientations.
  • Study the derivation of the electric potential formula for dipoles.
  • Explore the implications of neglecting higher-order terms in dipole approximations.
  • Investigate the use of diagrams in visualizing electric fields and potentials.
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone seeking to understand electric potential calculations involving dipoles.

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Homework Statement


Calculate the electric potential due to a tiny dipole whose dipole moment is 6.0×10^−30 C*m at a point 3.6×10^−9 m away for the following cases.

a) This point is along the axis of the dipole nearer the positive charge.

b) This point is 45 degrees above the axis but nearer the positive charge.

c) This point is 45 degrees above the axis but nearer the negative charge. Let V = 0 at r = infinity .


Homework Equations



For part a) I used p = q*d, where p is the dipole moment, q is the charge, and d is displacement. Then used (1/(4*pi*E))*(q/d), where E is the permittivity of free space constant, 8.85 x 10^-12

For part b) I got stuck on this part, I know I have to use the given 45 degrees, perhaps to find a new value for d?

Im not as familiar as I would like to be with the subject, any help or explanation welcome.

The Attempt at a Solution



a) V = 4.2 x 10^-3
b) V = ?
c) V = ?
 
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for part b and c:
1.draw a neat diagram.
2.calculate the distance of the point at which the potential is to be calculated from each charged end of the dipole.
3. assume the charge and the separation of the charges of dipole.
4.relate this with the dipole moment given ( u can replace this in the eqn. u find later).
5.now find the potential at the point due each charge ( remember to take opposite sign of potential for +ve and -ve charges of the dipole).
6 add this to get the result.
** as the dipole is tiny, may be, u will require to neglect square and higher power of l, the separation of charges of dipole or any other approximation of the sort. i have'nt done the problem physically, so i cannot be certain.
 

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