Question

What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1)?


What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1)? 

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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

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Answer #1

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

Please upvote.

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