Electric field strength at a point between charges

[radiant_june]

Find the electric field strength at point B between two charges shown below:

Given/Known Values
q₁ = 4.0×10^-6 C
r₁ = 40 cm = 0.4 m (Distance from q₁ to point B)
q₂ = -1.0×10^-6 C
r₂ = 30 cm = 0.3 m (Distance from q₂ to point B)
k = 9.0×10⁹ Nm²/C²

Equations

Electric Force:

F_E = (k⋅q₁⋅q₂)/r²
F_E = q⋅E​

Electric Field:

E = (k⋅q)/r²​

My thought process was that I could find the electric field strengths of both charges, and then find the difference between them, since point B is between the two charges.

E₁ = (k⋅q₁)/r₁²
= (9.0×10⁹⋅4.0×10^-6)/0.4²
= 225000 N/C

E₂ = (k⋅q₂)/r₂²
= (9.0×10⁹⋅-1.0×10^-6)/0.3²
= -100000 N/C

ΔE = E_B = E₁ - E₂
= 225000 - (-100000)
= 325000 N/C

I'm not really sure if this is the correct way of finding the electric field strength of point B. Any help would be appreciated!

 

[tnich]

Find the electric field strength at point B between two charges shown below:

Given/Known Values
q₁ = 4.0×10^-6 C
r₁ = 40 cm = 0.4 m (Distance from q₁ to point B)
q₂ = -1.0×10^-6 C
r₂ = 30 cm = 0.3 m (Distance from q₂ to point B)
k = 9.0×10⁹ Nm²/C²

Equations

Electric Force:

F_E = (k⋅q₁⋅q₂)/r²
F_E = q⋅E​

Electric Field:

E = (k⋅q)/r²​

My thought process was that I could find the electric field strengths of both charges, and then find the difference between them, since point B is between the two charges.

E₁ = (k⋅q₁)/r₁²
= (9.0×10⁹⋅4.0×10^-6)/0.4²
= 225000 N/C

E₂ = (k⋅q₂)/r₂²
= (9.0×10⁹⋅-1.0×10^-6)/0.3²
= -100000 N/C

ΔE = E_B = E₁ - E₂
= 225000 - (-100000)
= 325000 N/C

I'm not really sure if this is the correct way of finding the electric field strength of point B. Any help would be appreciated!

I get the same numerical answer. To complete the problem, you need to specify the direction of the $\vec E$ vector.