Two point charges of equal magnitude are 7.5 cm apart. at the midpoint of the line connecting them, their combined electric field has magnitude of 45 n/c. find the magnitude of the charges. pls show me the complete calculation,

We know that the electric field generated by to charges at a certain point between them is given by:
E = 1/(4πε₀) · (q₂ / d₂² - q₁ / d₁²)
Please note that distances must be in [m] in order to have the correct units of measurements.

In our case, we are at the midpoint between the two charges, therefore d₁ = d₂ = d and:
E = 1/(4πε₀d²) · (q₂ - q₁)

In order for the term (q₂ - q₁) to be ≠0, since the two charges have equal magnitude, they must be of opposite sign. For convenience, we decide 
q₂ = q 
q₁ = -q

Therefore we get:
E = 1/(4πε₀d²) · (q - (-q)) = 1/(4πε₀d²) · (2q) =  q / (2πε₀d²)

We now solve for charge q:
q = 2π · ε₀ · d² · E
   = 2π · (8.854×10⁻¹²) · (3.75×10⁻²)² · (45)
   = 3.52×10⁻¹²C

Therefore:
q₂ = +3.52×10⁻¹²C
q₁ = -3.52×10⁻¹²C

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