This questions has 6 parts: Two charges, Q 1 = 3.70 ?C, and Q 2 = 6.10 ?C are lo

Question

This questions has 6 parts:

Two charges, Q1= 3.70 ?C, and Q2= 6.10 ?C are located at points (0,-3.00 cm ) and (0,+3.00 cm), as shown in the figure.

a) What is the magnitude of the electric field at point P, located at (6.50 cm, 0), due to Q1 alone?

b) What is the x-component of the total electric field at P?

c) What is the y-component of the total electric field at P?

d) What is the magnitude of the total electric field at P?

e) Now let Q2 = Q1 = 3.70 ?C. Note that the problem now has a symmetry that you should exploit in your solution. What is the magnitude of the total electric field at P?

f) Given the symmetric situation of the previous problem, what is the magnitude of the force on an electron placed at point P?

Please help! Thank you so much in advance!

Explanation / Answer

a) KQ1 / r2 = (9 * 10^9 * 3.70 * 10^(-6) ) / ((sqrt(3^2 + 6.5^2) * 10^(-2) )^2 = 6497560.9756 N/coulomb

= 6.5 * 106 N/coulomb

KQ1 / r12 =  (9 * 10^9 * 3.70 * 10^(-6) ) / ((sqrt(3^2 + 6.5^2) * 10^(-2) )^2 = 6497560.9756

KQ2 / r22 = (9 * 10^9 * 6.10 * 10^(-6) ) / ((sqrt(3^2 + 6.5^2) * 10^(-2) )^2 = 10712195.12195

(b) In X-dir

cos Q = 6.5/sqrt(3^2 + 6.5^2) = 0.907959

(6497560.9756 + 10712195.12195)*cos Q = 15625752.93657 N/coulomb = 1.56 * 107 N/coulomb

(c) In Y-dir

sin Q = 3/sqrt(3^2 + 6.5^2) = 0.419

(10712195.12195 - 6497560.9756 )*sin Q = 1765931.7073 N/coulomb = 1.766 * 106 N/coulomb

d) sqrt(15625752.93657^2 + 1765931.7073^2) = 15725223.993 N/coulomb = 1.57 * 107 N/coulomb

e) In this case there will be no y-component due to symmetry-

Both will produce same electric field=  KQ / r2 = (9 * 10^9 * 3.70 * 10^(-6) ) / ((sqrt(3^2 + 6.5^2) * 10^(-2) )^2 = 6497560.9756 N/coulomb

(6497560.9756 + 6497560.9756)*cos Q = 11799037.93169 N/coulomb = 1.18 * 107 N/coulomb

f) Force = q*E = 1.6 * 10^(-19) * 11799037.93169 = 1.89 * 10-12N in negative X direction.

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