Consider the situation shown in the Figure. The charges are q 1 = 1.0 ?C (bottom
ID: 2290541 • Letter: C
Question
Consider the situation shown in the Figure. The charges are q1 = 1.0 ?C (bottom left chrge), q2 = 6.0 ?C , and q3 = -1.0 ?C (top charge). The distances are a =1.00cm, b =2.50cm, and c =1.60cm. Point "X" is at the top left corner, a distance c away from q1 and a distance a away from q3.
(a) What is in N/C the magnitude of the electrical field at point "X" due to the bottom left charge (q1)?
(b) What is in degrees the direction of the electrical field at point "X" due to the bottom left charge (q1)?
(c) What is in degrees the direction of the electrical field at point "X" due to the top charge (q3)?
(d) What is in N/C the magnitude of the electrical field at point "X" due to all charges?
(e) What is in degrees the direction of the electrical field at point "X" due to all charges?
Express directions in degrees relative to the traditional positive direction and measured in the counterclockwise direction.
MUST SHOW FULL WORK WITH NUMBERS
Explanation / Answer
a) E1 = k*q1/c^2
= 9*10^9*1*10^-6/0.016^2
= 3.516*10^7 N/c <<<<<<<------Answer
b) theta = tan^-1(0.016/0.01)
= 58 degrees with +x axis. <<<<<<<------Answer
c) 0 degrees with +x axis. i.e towards +x axis <<<<<<<------Answer
d)
E2 = k*q2/((a+b)^2 + c^2)
= 9*10^9*6*10^-6/((0.01+0.025)^2 + 0.016^2)
= 3.65*10^7 N/c
direction, theta = tan^-1((1+2.5)/1.6)
= 114 degrees with +x axis.
E3 = k*q3/c^2
= 9*10^9*1*10^-6/0.016^2
= 3.52*10^7 N/c towards +x axis.
Ex = E1*cos(58) + E2*cos(114) + E3*cos(0)
= 3.95*10^7 N/c
Ey = E1*sin(58) + E2*sin(114) + E3*sin(0)
= 6.32*10^7 N/c
E = sqrt(Ex^2+Ey^2)
= 7.45*10^7 N/c <<<<<<<------Answer
e)
directon, theta = tan^-1(Ey/Ex)
= tan^-1(6.32/3.95)
= 58 degrees with +x axis <<<<<<<------Answer