A charge of #1 C# is at #(-2,7,1)# and a charge of #2 C# is at #(0,-4 ,4) #. If both coordinates are in meters, what is the force between the charges?

Question

A charge of #1 C# is at #(-2,7,1)# and a charge of #2 C# is at #(0,-4  ,4)  #. If both coordinates are in meters, what is the force between the charges?

Benjamin Asiedu · Accepted Answer

#1.3433 imes 10^8\ N# The distance #d# between two points #(-2, 7, 1)# & #(0, -4, 4)# is given by distance formula #d=\sqrt{(-2-0)^2+(7-(-4))^2+(1-4)^2}=\sqrt134# Now, the electrostatic force #F# between the point charges #Q_1=1C# & #Q_2=2 C# at a distance #d=\sqrt134# #F=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{d^2}# #=(9 imes 10^9)\frac{1\cdot 2}{(\sqrt134)^2}# #=1.3433 imes 10^8\ N#

Xavier Adame · Answer

undefined To calculate the force between the charges, we use Coulomb's law, which states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

Let's denote the position vectors of the charges as r1 = (-2, 7, 1) and r2 = (0, -4, 4). The distance between the charges is given by the magnitude of the vector difference between their positions, |r2 - r1|.

Using the formula for the magnitude of a vector, the distance between the charges is:
|r2 - r1| = sqrt((0 - (-2))^2 + (-4 - 7)^2 + (4 - 1)^2)

Now, calculate the magnitude of the distance vector and plug it into Coulomb's law:

|F| = (k * |q1 * q2|) / |r2 - r1|^2

Where:
k is Coulomb's constant (8.9875 × 10^9 N m^2/C^2)
q1 = 1 C
q2 = 2 C

Now, calculate |F| using the given values.