An electric field measured near a point charge of 3.0 X 10^-6 C has a strength of 1.50 X 10^5 N/C How far is the point from the source charge

To find the distance from the point charge, we can use the formula for the electric field due to a point charge:

E = k * (q / r^2)

Where:
E is the electric field strength
k is the Coulomb's constant (approximately 9.0 x 10^9 N m^2 / C^2)
q is the source charge
r is the distance from the source charge to the point where the electric field is measured

Rearranging the formula to solve for r, we have:

r = √(k * (q / E))

Plugging in the values given in the problem:
q = 3.0 x 10^-6 C (source charge)
E = 1.50 x 10^5 N/C (electric field strength)
k = 9.0 x 10^9 N m^2 / C^2 (Coulomb's constant)

Let's calculate the value of r:

r = √(9.0 x 10^9 N m^2 / C^2 * (3.0 x 10^-6 C / 1.50 x 10^5 N/C))

First, we simplify the product inside the square root:

r = √(9.0 x 10^9 N m^2 / C^2 * (3.0 x 10^-6 C / 1.50 x 10^5 N/C))
r = √((9.0 x 10^9 N m^2 / C^2) * (2.0 x 10^-11))
r = √(18 x 10^-2)
r = √(1.8 x 10^-1)

Next, we calculate the square root:

r = √(1.8 x 10^-1)
r ≈ 0.424

So, the distance from the point charge is approximately 0.424 meters.

E=q/r^2

r=sqrt(q/E)