A dust particle carrying a charge of -3 x 10-10 C is 2mm to the left of another dust particle carrying a charge of +4 x 10-10C. Find the magnitude and direction of the electric force on the first particle.
opposite charges attract so force to the left
d = 0.002 meter
k = 9*10^9
-k Q1Q2/d^2
oh, sorry, did not read carefully. They want force on FIRST so equal and opposite, to the right, positive
To find the magnitude and direction of the electric force on the first particle, we can use Coulomb's law:
Coulomb's law states that the magnitude of the electric force between two charged particles is given by:
F = (k * |q1 * q2|) / r^2
Where:
F is the electric force
k is Coulomb's constant, approximately equal to 9 x 10^9 N·m^2/C^2
|q1 * q2| is the product of the magnitudes of the charges
r is the distance between the charges
Given:
q1 = -3 x 10^-10 C (charge of the first particle)
q2 = +4 x 10^-10 C (charge of the second particle)
r = 2 mm = 2 x 10^-3 m (distance between the particles)
First, calculate |q1 * q2|:
|q1 * q2| = |-3 x 10^-10 C * +4 x 10^-10 C|
= |12 x 10^-20 C^2|
= 12 x 10^-20 C^2
Next, substitute the values into Coulomb's law:
F = (k * |q1 * q2|) / r^2
= (9 x 10^9 N·m^2/C^2 * 12 x 10^-20 C^2) / (2 x 10^-3 m)^2
= (108 x 10^-11 N·m^2) / (4 x 10^-6 m^2)
= 27 x 10^-5 N
So, the magnitude of the electric force on the first particle is 27 x 10^-5 N.
To find the direction of the force, we consider that like charges repel each other, and opposite charges attract each other.
Since the first particle (q1) carries a negative charge, and the second particle (q2) carries a positive charge, they will attract each other.
Therefore, the electric force on the first particle is directed towards the second particle, to the right.
To find the magnitude and direction of the electric force on the first dust particle, we can use Coulomb's Law. Coulomb's Law states that the electric force between two charged objects is directly proportional to the product of their charges 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 electric force
k is the electrostatic constant, approximately 9 x 10^9 N m^2/C^2
q1 and q2 are the charges of the particles
r is the distance between the particles
Let's substitute the given values into the equation:
F = (9 x 10^9 N m^2/C^2) * (|-3 x 10^-10 C| * |4 x 10^-10 C|) / (0.002 m)^2
= (9 x 10^9 N m^2/C^2) * (1.2 x 10^-19 C^2) / 0.000004 m^2
= (9 x 10^9 N m^2/C^2) * (1.2 x 10^-19 C^2) / 4 x 10^-6 m^2
= (9 x 1.2) / (4 x 10^-6) N
= 32.4 / (4 x 10^-6) N
= 8.1 x 10^6 N
Therefore, the magnitude of the electric force on the first dust particle is 8.1 x 10^6 Newtons.
To determine the direction of the electric force, we need to know whether the force is attractive or repulsive. Since the two particles have opposite charges (negative and positive), the electric force between them is attractive. Therefore, the direction of the electric force on the first dust particle is towards the second dust particle, pointing to the right.