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soupastupid
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Homework Statement
We know the magnitude of the electric field at a location on the x-axis and at a location on the y axis, if we are far from the dipole.
(a) Find [tex]\Delta[/tex]V= V_p - V_a along a line perpendicular to the axis of a dipole. Do it two ways: from superposition of V due to the two charges and from the integral of the electric field.
(b) Find [tex]\Delta[/tex]V = V_c - V_d along the axis of the dipole. Include the correct signs. Do it two ways: from the superposition of V due to the two charges and from the integral of the electric field.
Homework Equations
V_q = (1/4[tex]\pi[/tex][tex]\epsilon[/tex]_0)(+or-q/r)
k= 1/4[tex]\pi[/tex][tex]\epsilon[/tex]_0
The Attempt at a Solution
(a)
superposition
[tex]\Delta[/tex]V= (1/4[tex]\pi[/tex][tex]\epsilon[/tex]_0)(+q/(d^2+(s^2)/4))^(1/2))-(1/4[tex]\pi[/tex][tex]\epsilon[/tex]_0)(-q/(d^2+(s^2)/4))^(1/2))
[tex]\Delta[/tex]V= 0
BUT
i don't kno how to do integral
i think its
integral from p to a : E times dd
how do i do it?
i thinks its...
int from a to b: kq/r^2
and i use formula:
int of 1 / x^2 + a^2 dx = (1/a)tan^-1 (x/a)
but I am not sure how to use it or show the answer
(b) superposition
[tex]\Delta[/tex]V = V_c - V_d
= (E_c)a - (E_d)b = 2kqsa/(a^3) -2kqsb/(b^3)
= ((sq)/(2[tex]\pi[/tex][tex]\epsilon[/tex]_0))(1/(a^2)-1(b^2))
but again
i don't kno how to do integration
i haven't got a clue for part B
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