Two point charges of 2.0 nC and 6.0 nC are both located 1.0 m away from a third charge of 3.0 nC ("n" is the metric prefix "nano" and means 10^-9) as shown. What is the electric force (magnitude and direction) on the 3.0 nC charge?
3.0 nC
O---------O 6.0 nC
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O 2.0 nC
The 3.0 nC charge experiences a force up of k*6*3*10^-18 N and a force to the left of
k*2*3*10^-18 N
k is the Coulomb constant.
Add the two forces as vectors.
To find the electric force on the 3.0 nC charge, we can use Coulomb's law. Coulomb's law states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
First, let's find the distance between the 3.0 nC charge and the 6.0 nC charge. It is given as 1.0 m.
Next, we can calculate the electric force between the 3.0 nC and 6.0 nC charges using Coulomb's law:
Electric Force = (k * q1 * q2) / r^2
Where:
k = Coulomb's constant = 9 x 10^9 N m^2/C^2
q1 = charge of the 3.0 nC charge = 3.0 x 10^-9 C
q2 = charge of the 6.0 nC charge = 6.0 x 10^-9 C
r = distance between the charges = 1.0 m
Plugging in the values, we get:
Electric Force = (9 x 10^9 N m^2/C^2 * (3.0 x 10^-9 C) * (6.0 x 10^-9 C)) / (1.0 m)^2
Simplifying the expression, we get:
Electric Force = 108 N
So, the electric force on the 3.0 nC charge is 108 N.
To determine the direction of the force, we can use the principle that like charges repel each other and opposite charges attract each other. In this case, the 3.0 nC and 6.0 nC charges have opposite signs, so they will attract each other. The force will act towards the 6.0 nC charge.
Therefore, the magnitude of the electric force on the 3.0 nC charge is 108 N, and the direction of the force is towards the 6.0 nC charge.