What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1)?
Part A
Give your answer in component form. (Assume that x-axis is horisontal and points to the right, and y-axis points upward.)
Part B
Give your answer as a magnitude and angle measured cw from the positive x-axis.
Part C
Express your answer using two significant figures ΑΣφ A2op CW from the axis Submit Request Answer
given,
Suppose Charge q1 = 5nC = 5*10-9 C
q2 = 5nC = -5*10-9 C
q3 = 10nC = 10*10-9C
r1 = distance between q1 and dot = 4 cm = 0.04 m
r2 = distance between q2 and dot = 2 cm = 0.02 m
r3 = distance between q3 and dot
r3 = sqrt [(4cm)^2+(2cm)^2] = 4.47 cm = 0.0447 m
= 26.6 deg
Because, tan() = r1/r2
= arctan(2/4) = 26.6 deg
Now Since Electric field is given by,
E = k*q/r^2
where, k = 9*10^9
q = charge that produce electric field
r = distance from point
So, electric field at dot due to q1
E1 = k*q1/r1^2
E1= [9*10^9*5*10^-9]/(2*10^-2)^2
E1 = 11.25*10^4 N/C along +ve x-axis.
Electric field at dot due to q2
E2 = k*q2/r2^2
E2 = [9*10^9*5*10^-9]/(4*10^-2)^2
E2 = 2.8125*10^4N/C along +ve y-axis.
Electric field at dot due to q3
E3 = k*q3/r3^2
E3= [9*10^9*10*10^-9]/(4.47*10^-2)^2
E3 = 4.5*10^4 N/C at 26.6 with -ve y-axis.
Now x component of net electric field
Ex = E1+E3x
Ex = 11.25*10^4 N/C + 4.50*10^4 N/C*sin(26.60 deg)
Ex = 13.27*10^4 N/C
y component of net electric field
Ey = E2 − E3y
Ey = 2.8125*10^4 N/C − 4.50*10^4N/C*cos(26.60 deg)
Ey = -1.21*10^4N/C
part A)
So, net electric field(E) = Ex i + Ey j
E = 13*10^4 i - 1.2*10^4 j
Part-B)
Magnitude of net electric field
E = sqrt [Ex^2+Ey^2]
E = sqrt[(13.27*10^4)^2 + (-1.21*10^4)^2]
E = 13.32*10^4 N/C
Part-C)
Direction
= arctan(Ey/Ex)
= arctan((-1.21*10^4)/(13.27*10^4)) = -5.21 deg
= -5.2 deg below x-axis
Direction = 5.2 deg CW from the +x-axis
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