Question

A long uniformly charged thread (linear charge density ? = 1.8 C/m ) lies along the x axis in the figure.(Figure 1) A small charged sphere (Q = -2.1 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?

Answer 1

The distance from sphere to point (7,7)

d = sqrt((0.07)²+ (0.07 + 0.05)²)

d = 0.1389244

E = 9e9*2.1 / 0.0193

E = - 9.793e11

? = tan^-10.12 /0.07 = 59.74

so, E_x = -9.793e11 * cos 59.74 = -4.935e11

E_y = -9.793e11 * sin 59.74 = -8.459e11

Also, Due to string

E_y = 2*9e9*1.8 / 0 .07 = 4.629e11

Therefore,

|E| = sqrt ((-4.935e11)² + (-8.459e11 + 4.629e11)²

|E| = sqrt ((-4.935e11)² + (-3.83E11)²

|E| = 6.247E11 N/C

Direction

? = tan^-1 (3.83 / 4.935)
? = 37.81 degree below the negative x -axis