The strength of an electric field at 5.0 cm from a point charge is 100.0 N/C. What is the magnitude of the source charge? Show work so I understand how to do it.
If I knew how to do it with formula I would have done it.
Rearrange the formula to calculate Q, using algebra. You get
Q = r^2*E/k
k = 8.99*10^9 N*m^2/C^2
(a constant of nature)
E = 100 N/C
r = 0.05 m
Just crank out the number. It will be in Coulombs.
E=kQ/r^2
solve for Q, you have r, E
To find the magnitude of the source charge, we can use Coulomb's law, which relates the electric field strength (E) to the source charge (Q) and the distance (r) from the charge.
Coulomb's law states that the electric field strength is proportional to the magnitude of the source charge and inversely proportional to the square of the distance from the charge. Mathematically, it can be expressed as:
E = k * (|Q| / r^2),
where E is the electric field strength, k is Coulomb's constant (approximated as 9 x 10^9 N m^2/C^2), |Q| is the magnitude of the source charge, and r is the distance from the charge.
Given that the electric field strength (E) is 100.0 N/C and the distance (r) is 5.0 cm (which is 0.05 m), we can plug these values into Coulomb's law and solve for |Q|.
100.0 N/C = (9 x 10^9 N m^2/C^2) * (|Q| / (0.05 m)^2).
Now, we can rearrange the equation to solve for |Q|:
|Q| = (100.0 N/C) * ((0.05 m)^2) / (9 x 10^9 N m^2/C^2).
Evaluating this expression will give us the magnitude of the source charge.
Calculating the expression:
|Q| = (100.0 N/C) * (0.0025 m^2) / (9 x 10^9 N m^2/C^2).
|Q| = 2.78 x 10^-14 C.
The magnitude of the source charge is approximately 2.78 x 10^-14 C.