A long uniformly charged thread (linear charge density = 2.0 C/m ) lies along th
ID: 1877049 • Letter: A
Question
A long uniformly charged thread (linear charge density = 2.0 C/m ) lies along the x axis in the figure.(Figure 1) A small charged sphere (Q = -2.4 C ) is at the point x=0cm, y=5.0cm.What is the direction of the electric field at the point x=7.0cm, y=7.0cm? E thread and E Q represent fields due to the long thread and the charge Q, respectively.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.
Explanation / Answer
givenlong uniformly charged
lamdba = 2 C/m
lies alogn x axis
Q = -2.4 C
lies at x = 0 cm, y = -5 cm
a. at x = 7 cm, y = 7 cm
Etherad = 2k*lambda/y = 2*8.98*10^9*2/0.07 = 513.1428*10^9 N/C ( in j direction ( y axis))
Echarge = kQ(xi + (y + 0.05)j)/(x^2 + (y + 0.05)^2)^3/2 = [-562.6646i - 964.568 j]*10^9 N/C
hence
Enet = [-562.6646i - 451.425 j]*10^9 N/C
Magnitude |E| = 721.37043 N/C
direction = arctan(Ey/Ex) = 218.74 deg CCW form +x axis