potential due to electric dipole is V = p.r / 4(pi)(epsilon)r^{3} show the tangential component of the electrical field is = psin(theta) / 4(pi)(epsilon)r^{3} what ive tried: i assumed there are 2 charges separated by distance r potential difference U = qV = -qE.r so can i say E[tangential] = V/r ?
well E = -(grad)V so could if i use d/dr? and get E = = -psin(theta) / 4(pi)(epsilon)r^{3} would i then just take E[tan] = Esin(theta) if we assume the dipole is at an angle theta to the E field? but what about the - sign
Right. You want the tangential component. Hint: [tex]\vec{p}\cdot \vec{r} = pr \cos\theta[/tex] How do you take the derivative in the tangential direction?
i'm not sure on how to do a tangential derivative...i may have done it in maths but didn't know thats what it was called. is it related to spherical coords?
okay s if i use 1/r*d/dtheta then Etan becomes = -(-psin(theta) / 4(pi)(epsilon)r^{3}) okay i get that now...thanks btw just so i can get the physical pic in my head, is the tangental component of V perpendicular to the moment 'bar', or is it simply horizontal? cause i pictured the diagram to be as seen in attached so i'm not sure how it is prcos if not horizontal
Imagine that the dipole moment defines the z-axis. The field at any point (specified by the position vector r) will have components in all directions. The one we want is the tangential component, perpendicular to the position vector at any point. (In spherical coordinates, it will be the theta component.) Note that pr cosθ is just the magnitude of the dot product of the vectors p and r that appears in the potential.
oh yeah... of courseshould have realised that earlier... thanks for the help, thats another revision topic i can tick off btw one quick question unrelated - i'm doing a question at the moment that simply states that there is a laser beam with power = 15MW/m^2 and i need to give the peak amplitude of the electric field n the beam... this question says its worth 10marks so the answer can't simply be power is proportional to the amplitude^2 can it?
I assume that that's the average intensity of the beam. Sure it's proportional to the the amplitude of the E field, but what's the proportionality constant? Hint: Review the Poynting vector.