electric field derived from potential?

2007-05-20 8:28 am
1.two equal positive charges Q are at (0,a) and (0,-a),respectively.(a)find the potential V(x) at a point (x,0).(b)use V(x) to find the electric field along the x axis.
2.two point charges are located as follows:Q1=5μC is at r1=2i+3j-5k m and Q2=2μC is at r2=-i+4j+2k m.what is their potential energy?

回答 (1)

2007-05-21 4:35 am
✔ 最佳答案
1. The charge Q at (0,a) will give a potnetial at point (x,0) given by
V(x) = k.Q/sqrt(a^2+x^2)
where k is a constant(=9x10^9 N.m^2/C^2)
[sqrt stands for square-root]
By symmetry, the charge at (0,-a) also gives the same potnetial at (x,0)
thus the total potnetial V(x) = 2kQ/sqrt(a^2+x^2)
(b) Using E=-dV(x)/dx, you can calculate the required electric field E in terms of x
E(x) = 2kQx/(a^2+x^2)^(3/2)
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2. First calculate the charge separation along the x, y and z axis.
x-axis: 2-(-1) units = 3 units
y-axis: 3-4 units = -1 units
z-axis: -5-2 units = -7 units
The separation between the two charges, s = sqrt[3^2+(-1)^2+(-7)^2] units
The potential energy = k[Q1][Q2]/s
where k is defined as before. Substitute the value of Q1, Q2 and s into the equations to calculate the answer.


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