Question

Electric Field due to Two Point Charges C)2o19 the x and y components of the electric field as an ordesed pai. Express your answer in newtons per coulomb to theee significant figures. Keep in mind that an x component that polnts to the right is positive and a y component that points upward is positive View Available Hintls) I Periodic Table Two point charges are placed on the x axis (Figure 1)The first charge, g8.00 C, is placed a distance 16 0 m from the along the positive x axis, the second charge 600 C, is placed a distance 900 m from the orlgin along the N/C Part B Now assume that charge q, is negative g6C (Figure 2)What is the net electric Seld at the origin, point O Give the x and y components of the electric field as an ordered pair. Express your answer in newtons per coulomb to three significant figures. Keep in mind that an x component that points to the right is positive and a y component that points upward is positive. View Available Hins

Answer 1

Sol. A :- We have to calculate Electric field at Origin due to charge q₁ and q_2.

Net electric field at origin E_total = E₁ + E₂

Where E₁ and E₂ are electric field due to charge q₁ and q₂ respectively.

First we will calculate E₁ = $kq$₁$\vec{r}$₁ $\setminus \left | r \right |^3$   

  We have given in question q₁ = 8nC

And r₁ = 0$\hat{i}$ + 0$\hat{j}$ - 16$\hat{i}$ - 0$\hat{j}$ = -16$\hat{i}$ + 0$\hat{j}$

So magnitude of r₁ = 16

Putting in formula we get E₁ = $9\times 10^9\times 8\times 10^-^9\times 16(\hat{-i})\setminus 16^3$ = 9/32($\hat{-i}$)

Similarly, now calculating E₂,

We have q₂= 6nC

and r₂= 9$\hat{i}$

Putting in formula E₂ = Kq₂r₂/$\left | r \right |^3$

E₂ = $9\times 10^9\times 6\times 10^-^9\times 9\hat{i\setminus 9^3}$

Which is E₂ = 2/3$\hat{i}$

Now E_total = E₁ + E₂ = (2/3 - 9/32)$\hat{i}$ = 37/96 $\hat{i}$

So E_OX= 37/96 and E_OY = 0 ( because there is no y component in E_total)

Sol. B :- Now we have q₂ = -6nC

So E₂ = 2/3 ($\hat{-i}$)

There is no change in E₁ because q₁ is same.

So E_OX = (2/3 + 9/32)($\hat{-i}$)

E_OX = 91/96 ($\hat{-i}$)

E_OY is still zero as no component of y in E_Total.