Calculate the magnitude of the electric field at a field point 3.0m from a point charge, q=5.0uC
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the equation for electric field a distance r away from a point charge is represented as Kq/r^2 where K is coulomb's law constant, q is the charge, and r is the radius (or distance). You can now plug in your values into the equation. Remember that K is 1/(4πε0).
To calculate the magnitude of the electric field at a field point due to a point charge, you can use the formula:
E = k * q / r^2
where E is the electric field magnitude, k is the Coulomb's constant (8.99 * 10^9 N.m^2/C^2), q is the charge of the point charge, and r is the distance from the charge to the field point.
Given that the charge, q, is 5.0 uC (microcoulombs) and the distance, r, is 3.0m, we can substitute these values into the formula:
E = (8.99 * 10^9 N.m^2/C^2) * (5.0 * 10^-6 C) / (3.0m)^2
First, we need to convert the charge from microcoulombs to coulombs. Since 1 uC = 1 * 10^-6 C, we have:
E = (8.99 * 10^9 N.m^2/C^2) * (5.0 * 10^-6 C) / (3.0m)^2
E = (8.99 * 10^9 N.m^2/C^2) * (5.0 * 10^-6 * 10^0 C) / (3.0m)^2
E = (8.99 * 10^9 N.m^2/C^2) * (5.0 * 10^-6 * 10^0 C) / (3.0 * 3.0m * 3.0m)
E = (8.99 * 10^9 N.m^2) * (5.0 * 10^-6) / (9.0 * m^2)
E = 4.995 * 10^3 N/C
Therefore, the magnitude of the electric field at the field point is approximately 4.995 * 10^3 N/C.