To find the magnitude of the electric field at the origin due to the two charges, we can use the formula for the electric field created by a point charge:
Electric Field (E) = k * |q| / r^2
Where:
k is Coulomb's constant, approximately 8.99 x 10^9 N m^2/C^2
|q| is the magnitude of the charge in Coulombs
r is the distance from the charge to the point where we want to find the electric field
Let's calculate the electric field at the origin due to the +18 nC charge at x = 1.6 m:
Charge |q| = 18 nC = 18 x 10^(-9) C
Distance r1 = 1.6 m
Electric Field (E1) = (8.99 x 10^9 N m^2/C^2) * (18 x 10^(-9) C) / (1.6 m)^2
Now, let's calculate the electric field at the origin due to the -18 nC charge at x = -4.7 m:
Charge |q| = 18 nC = 18 x 10^(-9) C
Distance r2 = 4.7 m
Electric Field (E2) = (8.99 x 10^9 N m^2/C^2) * (18 x 10^(-9) C) / (4.7 m)^2
Now, since the electric field is a vector quantity, we need to consider both the magnitudes and directions of the electric fields created by the +18 nC and -18 nC charges.
The electric field at the origin (E_total) is the vector sum of E1 and E2:
E_total = E1 + E2
Now, calculate the magnitude of E_total:
|E_total| = √(E1^2 + E2^2)
Substitute the calculated values and compute |E_total| to one decimal place:
|E_total| ≈ 3.2 x 10^6 N/C
The magnitude of the electric field at the origin is approximately 3.2 x 10^6 N/C.