The electric field strength @ distance = 1.0 m from a point charge is 4.0 x 10^4 N/C. What is the Electric field strength @ 2.0 m from the same charge?
To find the electric field strength at a distance of 2.0 m from the point charge, we can use Coulomb's Law. Coulomb's Law states that the electric field strength at a distance from a point charge is directly proportional to the charge and inversely proportional to the square of the distance.
The formula for Coulomb's Law is given as:
E = k * (Q / r^2)
Where E is the electric field strength, k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), Q is the charge of the point charge, and r is the distance from the point charge.
In this case, we are given the electric field strength at a distance of 1.0 m from the point charge (E1 = 4.0 x 10^4 N/C). Let's substitute the given values into the formula:
4.0 x 10^4 N/C = (8.99 x 10^9 N m^2/C^2) * (Q / 1.0^2)
Simplifying the equation:
4.0 x 10^4 = (8.99 x 10^9) * Q
To find Q, isolate it:
Q = (4.0 x 10^4) / (8.99 x 10^9)
Now that we know the charge (Q) of the point charge, we can find the electric field strength at a distance of 2.0 m (E2).
Using the same formula, let's calculate E2:
E2 = (8.99 x 10^9 N m^2/C^2) * (Q / 2.0^2)
Substituting the value of Q we calculated earlier:
E2 = (8.99 x 10^9 N m^2/C^2) * [(4.0 x 10^4) / (8.99 x 10^9)] / 4.0
Simplifying the equation:
E2 = (4.0 x 10^4) / 2.0
E2 = 2.0 x 10^4 N/C
Therefore, the electric field strength at a distance of 2.0 m from the same charge is 2.0 x 10^4 N/C.