A semicircle of radius a is in the first and second quadrants, with the center o

Question

A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge Q is distributed uniformly around the right half of the semicircle in the following figure.(Figure 1)

Part A

What is the magnitude of the net electric field at the origin produced by this distribution of charge?

Express your answer in terms of the variables Q, a, constant , and electric constant 0.

Part B

What is the direction of the net electric field at the origin produced by this distribution of charge?

Figure 1 of 1

A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge Q is distributed uniformly around the right half of the semicircle in the following figure.(Figure 1)

Part A

What is the magnitude of the net electric field at the origin produced by this distribution of charge?

Express your answer in terms of the variables Q, a, constant , and electric constant 0.

|E| =

Part B

What is the direction of the net electric field at the origin produced by this distribution of charge?

+x direction x direction +y direction y direction another direction

Figure 1 of 1

Explanation / Answer

A)

charge per unit length on left arc, lamda1 = Q/(pi*a/2)

= 2*Q/(pi*a)

charge per unit length on right arc, lamda2 = -Q/(pi*a/2)

= -2*Q/(pi*a)

Electric filed due to positive arc, E1 = (1/(4*pi*epsilon))*(lamda1/a)(i-j)

= (1/(4*pi*epsilon))*(2Q/(pi*a^2))(i-j)

Electric filed due to negative arc, E2 = (1/(4*pi*epsilon))*(lamda2/a)(i+j)

= (1/(4*pi*epsilon))*(2Q/(pi*a^2))(i+j)

Enet = E1 + E2

= (1/(4*pi*epsilon))*(4Q/(pi*a^2))i

= Q/(pi^2*epsilon*a^2) i

B) +x direction

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