Exploring Electric Field & Potential of a Charge Dipole

[tag16]

Homework Statement

Consider the charge configuration described where two equal but opposite charges of magnitude Q. What is the magnitude of the electric field and the electric potential from the dipole as a function of the distance x from the center of the dipole perpendicular to the dipole moment?

Homework Equations

V= k$$\sum$$qi/ri

The Attempt at a Solution

E= (2aq cos$$\theta$$)/(4$$\pi$$$$\epsilon_0$$r^2)

V=( P cos$$\theta$$)/(4$$\pi$$$$\epsilon_0$$r)

is this totally wrong?

 

[anathema]

No, your equations are not totally wrong. However, there are a few things that could be improved upon.

Firstly, your equation for the electric field is missing a factor of Q. It should be E = (2aQcosθ)/(4πε0r^3). This is because the electric field is directly proportional to the magnitude of the charges.

Secondly, your equation for the electric potential is missing a factor of Q^2. It should be V = (Pcosθ)/(4πε0r^2). This is because the potential is directly proportional to the product of the two charges.

Lastly, it would be helpful to define your variables and explain any assumptions you are making. For example, what do a and P represent? What is the angle θ? Also, it is important to note that these equations are only valid for points along the perpendicular axis of the dipole. For points off this axis, the equations become more complex.

Overall, your attempt at a solution shows that you understand the basic concepts of electric field and potential for a dipole. However, it could be improved by clarifying your variables and making sure all necessary factors are included in the equations.

 

[tomcue]

No, your attempt at a solution is not totally wrong. However, there are a few things that could be clarified or improved upon:

1. The equation for electric potential that you have written is actually for the potential at a point on the equatorial plane of the dipole (the plane perpendicular to the dipole moment). To find the potential at a point on the axis of the dipole (perpendicular to the equatorial plane), you would use the equation V = Pcosθ/(4πε0r^2).

2. The equations you have written are for the electric field and potential at a distance r from the center of the dipole. To express them as a function of the distance x from the center of the dipole perpendicular to the dipole moment, you would need to substitute r with √(x^2 + a^2), where a is the distance between the two charges in the dipole.

3. Your equations assume that the distance x is much larger than the distance a between the charges in the dipole. If x is not much larger than a, the equations will not be accurate and you would need to use a more complex formula that takes into account the finite size of the dipole.

Overall, your attempt at a solution shows a good understanding of the concepts involved in calculating the electric field and potential of a dipole. However, it could be improved by clarifying the equations and taking into account the distance x from the dipole.