two point charge q1=50c , q2=10c are lactated at (-1,1,-3)m, and (3,1,0)m, respectivly. Find the force on q1.?
use the distance equation to find the distance.
for magnitude of force, coulomb'slaw.
To find the force on charge q1, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * |q1| * |q2|) / r^2
Where:
- F is the force between the charges
- k is the electrostatic constant, approximately equal to 8.99 x 10^9 Nm^2/C^2
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
In this case, |q1| = 50 C, |q2| = 10 C, and the distance between the charges can be calculated using the distance formula:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Where:
- (x1, y1, z1) are the coordinates of the first charge (-1, 1, -3) m
- (x2, y2, z2) are the coordinates of the second charge (3, 1, 0) m
Let's calculate the distance between the charges first:
r = sqrt((3 - (-1))^2 + (1 - 1)^2 + (0 - (-3))^2)
= sqrt(4^2 + 0^2 + 3^2)
= sqrt(16 + 0 + 9)
= sqrt(25)
= 5 m
Now, substitute the values into Coulomb's Law:
F = (k * |q1| * |q2|) / r^2
= (8.99 x 10^9 Nm^2/C^2 * 50 C * 10 C) / (5 m)^2
= (8.99 x 10^9 Nm^2/C^2 * 500 C^2) / 25 m^2
= (4495 x 10^9 Nm^2) / 25 m^2
= 179.8 x 10^9 N
So, the force on q1 is approximately 179.8 x 10^9 N.