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Which point line connecting the two charges is the total electric field due to the two charges equal to zero?
Two particles having charges q1= 0.500nC and q2 = 7.50nC are separated by a distance of 2.00 m.
At what point along the line connecting the two charges is the total electric field due to the two charges equal to zero?
Please help me and show steps.
Thank you
Using Coulomb's law, the total electric field is:
E = k Q1 / r_1^2 + k Q2 / r_2^2 = 0
Q1 / r_1^2 + Q2 / r_2^2 = 0
Now, we must choose our origin. let it be at 0.5. Therefore,
r_1 = r
r_2 = r - 2.00 m
where r is the point along the E-field is zero. Solving for r gives:
0.5 / r^2 + 7.5 / (r + 2)^2 = 0
0.5 / r^2 = -7.5 / (r - 2)^2
(r - 2)^2 = -15 r^2
15r^2 + r^2 - 4r - 4 = 0
4r^2 - r - 1 = 0
Using the quadratic formula, the solution is r = 0.64039.
Point Line Plane - YourTeacher.com - Geometry Help