What is the magnitude of the electric field 0.3 m from a 10-4 C point charge?
To find the magnitude of the electric field, we can use Coulomb's law, which states that the electric field created by a point charge is directly proportional to the charge and inversely proportional to the square of the distance.
Coulomb's law equation is given by:
E = k * (q / r^2)
Where:
E is the magnitude of the electric field
k is Coulomb's constant (approximated to 9 x 10^9 N⋅m^2/C^2)
q is the charge of the point charge in Coulombs
r is the distance from the point charge
In this case, the charge (q) is 10^-4 C, and the distance (r) is 0.3 m. Let's substitute these values into the equation to calculate the magnitude of the electric field:
E = (9 x 10^9 N⋅m^2/C^2) * (10^-4 C) / (0.3 m)^2
First, let's square the distance:
E = (9 x 10^9 N⋅m^2/C^2) * (10^-4 C) / (0.09 m^2)
Now, calculate the fraction:
E = (9 x 10^9 N⋅m^2/C^2) * (10^-4 C) / 0.09
Next, multiply the numerator:
E = (9 x 10^5 N⋅m^2/C) / 0.09
Now, divide the numerator by the denominator:
E = 1 x 10^7 N/C
Therefore, the magnitude of the electric field 0.3 m from a 10^-4 C point charge is 1 x 10^7 N/C.