What is the total charge on the semicircle What is the y com

What is the total charge on the semicircle?

What is the y component of the electric field at the origin?

1. considering a d@ angle part of arc at angle @.

then charge density lambda = - 1.39@

width of part of this arc = R d@

charge on that part, dq = - 1.39 R @ d@

integrating,

q = - 1.39 R @^2 /2

where @ is from 0 to pi.

q = - 1.39 (0.394) (pi ^2 - 0 )/ 2 = - 0.274 pi^2 uC or - 2.7 uC

2. for this part, field at centre.

dE = k dq / R^2 = 1.39 k R @ d@ / R^2

dE = 1.39 k @ d@ / R

y - component, dEy = dE sin@

dEy = (1.39 x 10^-6 x 9 x 10^9 / 0.394 ) @ sin@ d@

dEy = 31751.27 @ sin@ d@

inetegrating,

Ey = 31751.27 ( sin@ - @cos@)

where @ is from 0 to pi

Ey = 31751.27 [ sinpi - pi cospi - sin0 + 0 cos0 ]

Ey = 31751.27 x pi = 99750 N/C