what are the magnitude and direction of the force on a charge of
+ 2x 10^ -7 C that is 0.30m from a charge of -5 x 10^-7 C?
Since their charges are of opposite signs the attract each other.
F = k Q1 Q2 / d^2
= 9*10^9 * 2 * 5 * 10^-14 / 0.09
= 10^-2 Newtons
To find the magnitude and direction of the force between two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Given:
Charge 1 (q1) = +2x10^(-7) C
Charge 2 (q2) = -5x10^(-7) C
Distance (r) = 0.30 m
Step 1: Calculate the magnitude of the force using Coulomb's Law formula:
F = (k * q1 * q2) / r^2
Where:
k is the electrostatic constant and has a value of 9x10^9 N⋅m^2/C^2.
Plugging in the values:
F = (9x10^9 N⋅m^2/C^2) * (+2x10^(-7) C) * (-5x10^(-7) C) / (0.30 m)^2
F = -30 N
So, the magnitude of the force between the two charges is 30 N.
Step 2: Determine the direction of the force. The direction of the force is attractive if the charges have opposite signs and repulsive if they have the same sign.
In this case, one charge is positive (+2x10^(-7) C) and the other is negative (-5x10^(-7) C), so the force will be attractive.
Therefore, the force is 30 N in the direction from the negative charge to the positive charge.
To calculate the magnitude and direction of the force between two charges, 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 equation for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the magnitude of the force between the charges
- k is the electrostatic constant (9 x 10^9 N m^2/C^2)
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
Using this equation, we can calculate the magnitude of the force between the charges in this scenario:
|q1| = 2 x 10^-7 C
|q2| = -5 x 10^-7 C
r = 0.30 m
k = 9 x 10^9 N m^2/C^2
Plugging in the values, we have:
F = (9 x 10^9 N m^2/C^2) * ((2 x 10^-7 C) * (-5 x 10^-7 C)) / (0.30 m)^2
Simplifying the equation:
F = (9 x 10^9 N m^2/C^2) * (-10^-14 C^2) / 0.09 m^2
F = -10 N
Therefore, the magnitude of the force between the charges is 10 N. The negative sign indicates that the force is attractive, as opposite charges attract each other.
As for the direction of the force, since the charges have opposite signs, the force will be directed towards each other along the line connecting them. Therefore, the force acts from the charge of +2 x 10^-7 C towards the charge of -5 x 10^-7 C.