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Problem: A total charge Q = 3.6 μC is distributed uniformly over a quarter circle arc of radius a = 8.8 cm as shown.a) What is λ the linear charge density along the arc?b )What is Ex, the value of the x-component of the electric field at the origin (x,y) = (0,0)?c) What is Ey, the value of the y-component of the electric field at the origin (x,y) = (0,0)?d) How does the magnitude of the electric field at the origin for the quarter-circle arc you have just calculated comnpare to the electric field at the origin produced by a point charge Q = 3.6 μC located a distance a = 8.8 cm from the origin along a 45o line as shown in the figure?    A. The magnitude of the field from the point charge is less than that from the quarter-arc of charge.    B. The magnitude of the field from the point charge is equal to that from the quarter-arc of charge    C. The magnitude of the field from the point charge is greater than that from the quarter-arc of charge

FREE Expert Solution

Linear charge density:

λ=QL

a)

L = (π/2)a

Substituting to the equation for the linear charge density:

λ=3.6×10-6(π2)(8.8×10-2)

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Problem Details

A total charge Q = 3.6 μC is distributed uniformly over a quarter circle arc of radius a = 8.8 cm as shown.

Image for A total charge Q = 3.6 muC is distributed uniformly over a quarter circle arc of radius a = 8.8 cm as shown.

a) What is λ the linear charge density along the arc?

b )What is Ex, the value of the x-component of the electric field at the origin (x,y) = (0,0)?

c) What is Ey, the value of the y-component of the electric field at the origin (x,y) = (0,0)?Image for A total charge Q = 3.6 muC is distributed uniformly over a quarter circle arc of radius a = 8.8 cm as shown.

d) How does the magnitude of the electric field at the origin for the quarter-circle arc you have just calculated comnpare to the electric field at the origin produced by a point charge Q = 3.6 μC located a distance a = 8.8 cm from the origin along a 45o line as shown in the figure?

    A. The magnitude of the field from the point charge is less than that from the quarter-arc of charge.
    B. The magnitude of the field from the point charge is equal to that from the quarter-arc of charge
    C. The magnitude of the field from the point charge is greater than that from the quarter-arc of charge

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