Two charges q1= -25 C and q3= 4.0 C are placed 0.012 m apart. A third negative charge, q2 is placed a distance L from q1 as shown. If the net electric force on q2 is 0N what is the value of L?
To find the value of L, we need to use the concept of electrostatic force and Coulomb's law. Coulomb's law states that the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's calculate the magnitudes of the electrostatic forces between q1 and q2, and between q2 and q3.
We can use the equation:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electrostatic force between the charges,
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges (taking the absolute value since the charges are given as negative),
and r is the distance between the charges.
For the force between q1 and q2:
F1 = k * (|q1| * |q2|) / r1^2
Since the net electric force on q2 is 0N, the magnitudes of the forces exerted on q2 by q1 and q3 should be equal, so F1 = F2.
For the force between q2 and q3:
F2 = k * (|q2| * |q3|) / r2^2
Since F1 = F2, we can equate the two equations:
k * (|q1| * |q2|) / r1^2 = k * (|q2| * |q3|) / r2^2
The electrostatic constant (k) cancels out:
(|q1| * |q2|) / r1^2 = (|q2| * |q3|) / r2^2
Substituting the given values:
(|q1| * |q2|) / (0.012^2) = (|q2| * |q3|) / (L^2)
Simplifying the equation:
(25 * |q2|) / (0.012^2) = (|q2| * 4.0) / (L^2)
Simplifying further:
(25 * 8.99 x 10^9) / (0.012^2) = 4.0 / L^2
Now we can solve for L:
L^2 = (4.0 * (0.012^2)) / (25 * 8.99 x 10^9)
L^2 = 7.68 x 10^-14 / (224.75 x 10^9)
L^2 = 3.419 x 10^-24
Taking the square root of both sides:
L = sqrt(3.419 x 10^-24)
L = 5.84 x 10^-13 m
Therefore, the value of L is approximately 5.84 x 10^-13 meters.
To find the value of L, we need to analyze the forces acting on q2 and set the net force equal to zero.
The electric force between two charges q1 and q2 is given by Coulomb's law:
F12 = (k * |q1 * q2|) / r^2
where F12 is the force exerted by q1 on q2, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Considering the charges q1 and q2, the electric force exerted by q1 on q2 is attractive because they have opposite signs. Hence, the force F12 is directed towards q1.
Now, let's calculate the force F12 exerted by q1 on q2 using the given values:
F12 = (k * |q1 * q2|) / r^2
= (8.99 x 10^9 N m^2/C^2) * (25 C * q2) / (0.012 m)^2
The electric force between charges q2 and q3 is also given by Coulomb's law:
F23 = (k * |q2 * q3|) / r^2
Considering the charges q2 and q3, the electric force exerted by q3 on q2 is repulsive because they have the same sign. Hence, the force F23 is directed away from q3.
Now, let's calculate the force F23 exerted by q3 on q2 using the given values:
F23 = (k * |q2 * q3|) / r^2
= (8.99 x 10^9 N m^2/C^2) * (4 C * q2) / (0.012 m)^2
Since the net force on q2 is 0 N, the forces F12 and F23 have to cancel each other out:
F12 + F23 = 0
Substituting the calculated values of F12 and F23:
(8.99 x 10^9 N m^2/C^2) * (25 C * q2) / (0.012 m)^2 + (8.99 x 10^9 N m^2/C^2) * (4 C * q2) / (0.012 m)^2 = 0
Now we can solve this equation to find the value of q2. Once we find q2, we can use it to find L using trigonometry and the given distances.
as shown....?
you have to take the forces F12 adn F32 and add them as vectors.