Question

There is a uniform charge distribution of lambda = 4.699

Answer 1

First, start with:

dE= k*dQ/(r^2)

dQ= ? dL (dL is the change in length)

In the case of the semi-circle the distance from the center of the semicircle to the edge of the circle is radius of the circle

r= R

dE= k*? dL/(R^2)

Now we need to split this into x and y components, but the x component is zero due to symmetry so the y component remains:

dEy= dE sin(T) = (k*? dL/(R^2)) sin(T)

Now the arc length of a circle is

L= R*T
and
dL=R*dT

dEy = (k*? dT/R) sin(T)

Now for integration:

Ey= (k*?/R) int[sin(T) dT] (0,Pi)

Ey= (2*k*?/R)

And R= L/?

Ey= (2?*k*?/L)

Because Ex=0:

E= abs((2?*k*?/L))

E= 14746.67 N/C