Potential due to electric dipole

[indie452]

potential due to electric dipole is

V = p.r / 4(pi)(epsilon)r³

show the tangential component of the electrical field is

= psin(theta) / 4(pi)(epsilon)r³what I've 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 ?

 

[Doc Al]

How is electric field related to potential?

 

[indie452]

well E = -(grad)V
so could if i use d/dr? and get E = = -psin(theta) / 4(pi)(epsilon)r³

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

 

[Doc Al]

well E = -(grad)V

Right.

so could if i use d/dr?

You want the tangential component.

Hint: \vec{p}\cdot \vec{r} = pr \cos\theta

How do you take the derivative in the tangential direction?

 

[indie452]

i'm not sure on how to do a tangential derivative...i may have done it in maths but didn't know that's what it was called.
is it related to spherical coords?

 

[Doc Al]

i'm not sure on how to do a tangential derivative...i may have done it in maths but didn't know that's what it was called.
is it related to spherical coords?

Yes. Look here: http://en.wikipedia.org/wiki/Gradient#Non-Cartesian_Coordinate_Systems

 

[indie452]

okay s if i use 1/r*d/dtheta

then Etan becomes

= -(-psin(theta) / 4(pi)(epsilon)r³)

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

 

[Doc Al]

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.

 

[indie452]

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 realized that earlier...

thanks for the help, that's 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?

 

[Doc Al]

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.