A long uniformly charged thread (linear charge density = 2.5 C/m ) lies along th

Question

A long uniformly charged thread (linear charge density = 2.5 C/m ) lies along the x axis in the figure.(Figure 1)

A small charged sphere (Q = -2.3 C ) is at the point x=0cm, y=5.0cm.

1). What is the direction of the electric field at the point x=7.0cm, y=7.0cm? E_Q thread and E_Q represent fields due to the long thread and the charge Q, respectively.

Express your answer to two significant figures and include the appropriate units.

(Answer should be in degrees for number 1)

= (value) _________ (units)___________ counterclockwise from the +x axis

2). What is the magnitude of the electric field at the point x=7.0cm, y=7.0cm?

Express your answer to two significant figures and include the appropriate units.

(Answer should be in this form)

E =  (value) _________ (units)___________

Explanation / Answer

Ethready = lambda/(2*pi*e0*y) = 2.5/(2*pi*8.85*10^-12*0.07) = 6.42*10^11 N/C

Ethreadx = 0

r = sqrt(7^2+12^2) = 13.8 cm = 0.138m

tantheta = 12/7

theta = 59.7

EQx = -k*Q*costheta/r^2 = -(9*10^9*2.3*cos59.7)/0.138^2 = -5.5*10^11 N/C

EQy = -k*Q*sintheta/r^2 = -(9*10^9*2.3*sin59.7)/0.138^2 = -9.38*10^11 N/C

Ex =   -5.5*10^11

Ey = 6.42*10^11 - 9.38*10^11 = -2.96*10^11 N/C

direction = tan^-1(2.96*10^11/(5.5*10^11)) = 208.3 degrees counterclockwise from + axis

------------

(2)

magnitude = sqrt((5.5*10^11)^2+(2.96*10^11)^2) = 6.42*10^11 N/C

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