PLEASE PROVIDE FULL SOLUTIONS AND A DIAGRAM! YOU WILL GET FULL POINTS! The charg

Question

PLEASE PROVIDE FULL SOLUTIONS AND A DIAGRAM! YOU WILL GET FULL POINTS!

The charges are: are located at the vertex of equilateral triangle with the sides of 1.00 m Find total electric field and potential at the point C, which is a vertex of that triangle It a positive q3 = 5 muC charge is brought from infinity to that point. Find force acting on it and work required to bring this charge from infinity to that point. Calculate change of energy of the system when 5 muC is brought to that point. Is this position stable or not ? Explain your answer.

Explanation / Answer

1) E1 = k*q1/x^2 = 9*10^9*2*10^-6/1^2 = 18000 N/c

E2 = k*q2/x^2 = 9*10^9*4*10^-6/1^2 = 36000 N/c

angle between E1 and E2 is 60 degrees

Enet = sqrt(E1^2 + E2^2 + 2*E1*E2*cos(60))

= sqrt(18000^2 + 36000^2 + 2*18000*36000*cos(60))

= 47623.5 N/c

V1 = k*q1/x = 9*10^9*2*10^-6/1 = 18000 volts

V2 = k*q2/x = -9*10^9*4*10^-6/1 = -36000 volts

Vnet = V1 + V2

= 18000 - 36000

= -18000 volts

2) force acting on q3 is

F = q3*Enet

= 5*10^-6*47623.5

= 0.238 N

work done = q*Vnet

= -5*10^-6*18000

= -0.09 J

3)chnage in energy = -workdone

= +0.09 J

4) This point is not stable because net force acting on q3 is not zero.

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