Linear charge density:

$\overline{){\mathbf{\lambda}}{\mathbf{=}}\frac{\mathbf{Q}}{\mathbf{L}}}$

**a)**

L = (π/2)a

Substituting to the equation for the linear charge density:

$\mathit{\lambda}\mathbf{=}\frac{\mathbf{3}\mathbf{.}\mathbf{6}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}}{\mathbf{\left(}{\displaystyle \frac{\mathbf{\pi}}{\mathbf{2}}}\mathbf{\right)}\mathbf{(}\mathbf{8}\mathbf{.}\mathbf{8}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{)}}$

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 E_{x}, the value of the x-component of the electric field at the origin (x,y) = (0,0)?

c) What is E_{y}, 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 45^{o} 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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