How Do Point Charges Affect Electric Field Vectors at a Specific Location?

[sami23]

Homework Statement

Point charge q1= -5.00 is at the origin and point charge q2= +3.00 is on the -x axis at x= 3.00 cm. Point P is on the y-axis at y= 4.00 cm .

Calculate the electric fields E₁ and E₂ at point P due to the charges q₁ and q₂. Express your results in terms of unit vectors.

Homework Equations

r = sqrt(x² + y²)
hat{r} = (vec{r} /r = x hat{i} + y hat{j}) / r
vec{E} = (k * q)/r² hat{r}

The Attempt at a Solution

E₁ will be the vector from q₁ to point P
r = sqrt(0² + .04²) = .04 m

hat{r} = (0 hat{i} + .04 hat{j})/.04 = 0 hat{i} + 1 hat{j}

E₁ = (9*10⁹) * (-5.00*10^-9) / .04² (0 hat{i} + 1 hat{j})
= 0 hat{i} - 2.81*10⁴ hat{j}

i did the exact same steps to find E₂ and
E₂ = 6.47*10² hat{i} + 8.62*10² hat{j}

Am I doing something wrong? According to the steps I used because my answers are wrong and i even followed the way the steps were in the book.

 

[Doc Al]

Is q₂ at x = +3 cm or at x = -3 cm?

 

[sami23]

q₂ is at x=+3 cm = 0.03m

 

[Doc Al]

q₂ is at x=+3 cm = 0.03m

So how did you end up with a positive i-component?

 

[rdl]

I would first check the units of the given charges q1 and q2. It seems that they are given in units of Coulombs (C) rather than the standard unit of charge, which is the Coulomb (C). This could be a typo or a mistake in the problem itself. Assuming that the charges are indeed given in Coulombs, the calculations for E1 and E2 would be as follows:

E1 = (9*10^9 Nm^2/C^2) * (-5 C) / (0.04 m)^2 * (0 hat{i} + 1 hat{j})
= -1.125*10^12 N/C * 0 hat{i} - 1.125*10^12 N/C * 1 hat{j}
= -1.125*10^12 N/C * (0 hat{i} + 1 hat{j})

E2 = (9*10^9 Nm^2/C^2) * (3 C) / (0.06 m)^2 * (-1 hat{i} + 0 hat{j})
= 1.125*10^12 N/C * (-1 hat{i} + 0 hat{j})
= -1.125*10^12 N/C * (-1 hat{i})

So, the final results for E1 and E2 are:
E1 = -1.125*10^12 N/C * (0 hat{i} + 1 hat{j})
E2 = 1.125*10^12 N/C * (-1 hat{i})

Note that the unit vectors are in the direction of the electric field, so they should not be included in the final answer. Also, it is important to pay attention to the signs of the charges and the direction of the electric field vectors. In this case, the negative charge q1 creates an electric field pointing towards it, while the positive charge q2 creates an electric field pointing away from it. The final answer for E1 should have a negative sign, while the final answer for E2 should have a positive sign.