Question

A long uniformly charged thread (linear charge density λ= 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

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

Answer 1) The electric field at distance r from the thread is radial and has magnitude

E = λ / (2 π ε° r)

The electric field from the point charge usually is observed to follow coulomb's law:

E = Q / (4 π ε°
`r^(2)`)

Now, adding the two field vectors:

`E_(thread)` = {2.5 / (22 π ε° X 0.07 ) ; 0}

Answer 2)
`E_(q)` = {2.3 / (4 2 π ε°) ( - 7/ (√(84); -12 / (√84))

Adding these two vectors will give the length which is magnitude of the combined field.

The y-component / x-component gives the tangent of the angle with the positive x-axes.

Please refer the graph and the attachment for better understanding.