Does anyone know how to calculate these questions?
Do your own work, show what you did and where you got stuck, and then you'll get plenty of help.
E = V / d (E is electric field strength; V is potential difference; d is separation distance);
W = Q x V (W is workdone; Q is charge; V is potential difference);
Thus, E = W / Q / d = W / (Q x d) and d = 4.0 m;
But I don't know the value of W. How can I find the value of electric field strength at P?
You are dealing with point charges here: Look up expressions for the electric field and electric potential at a given distance from a point charge. Note that electric field is a vector, but potential is a scalar.
E = Q / (4 pi eo r^2)
For +Q, E1 = Q / (4 pi eo 4^2) = Q / (64 pi eo)
For -Q, E2 = -Q / (4 pi eo 4^2) = -Q / (64 pi eo)
E1 + E2 = ?
V = Q / (4 pi eo r)
For +Q, V1 = Q / (4 pi eo 4) = Q / (16 pi eo)
For -Q, V2 = -Q / (4 pi eo 4) = -Q / (16 pi eo)
V1 + V2 = 0 and so this is the correct answer?
Electric field is a vector, so direction counts. Add them like vectors.
|E| = sqrt (E1^2 + E2^2)
E1 = 2 / (64 x 3.14 x 8.854 x 10^-12)
E2 = -E1
= sqrt (E1^2 + (-E1)^2)
= sqrt (2 x E1^2)
= sqrt (2 x (2 / (64 x 3.14 x 8.854 x 10^-12))^2)
= 15.90 x 10^8 V/m
(But the answer isn't correct)
That would be true if E1 and E2 were perpendicular, but they are not. Consider the horizontal & vertical components of each.
Let theta be the angle between the horizontal line and the hypotenuse,
sin theta = 1 / 4 = 0.25
Take right/upward directions as positive and left/downward directions as negative,
For +Q, component of E = E cos theta
For -Q, component of E = -E cos theta
Their sums = E cos theta - E cos theta = 0
For +Q, component of E = -E sin theta
For -Q, component of E = -E sin theta
Their sums = -E sin theta -E sin theta = -2E sin theta
|E| = |Horizontal Component of E| + |Vertical Component of E|
= sqrt ((Horizontal Component of E)^2 + (Vertical Component of E)^2)
= sqrt (0^2 + (-2E sin theta)^2)
= 2E sin theta
= 2E (0.25)
= E / 2
= 5.6 x 10^8 V/m
Am I correct?
You got it!
Typo here; this should be:
|E|^2 = |Horizontal Component of E|^2 + |Vertical Component of E|^2
Thank you very much!
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