a negative charge, $q_1$, of 6 $mu$c is 0.002 m north of a positive charge, $q_2$, of 3 $mu$c. what is the…

a negative charge, $q_1$, of 6 $mu$c is 0.002 m north of a positive charge, $q_2$, of 3 $mu$c. what is the magnitude and direction of the electrical force, $f_e$, applied by $q_1$ on $q_2$?\n\nmagnitude: $8\times10^{1}$ n\ndirection: south\n\nmagnitude: $8\times10^{1}$ n\ndirection: north\n\nmagnitude: $4\times10^{4}$ n\ndirection: south\n\nmagnitude: $4\times10^{4}$ n\ndirection: north

a negative charge, $q_1$, of 6 $mu$c is 0.002 m north of a positive charge, $q_2$, of 3 $mu$c. what is the magnitude and direction of the electrical force, $f_e$, applied by $q_1$ on $q_2$?\n\nmagnitude: $8\times10^{1}$ n\ndirection: south\n\nmagnitude: $8\times10^{1}$ n\ndirection: north\n\nmagnitude: $4\times10^{4}$ n\ndirection: south\n\nmagnitude: $4\times10^{4}$ n\ndirection: north

Answer

Explanation:

Step1: Identify Coulomb's law formula

The formula for the electric - force between two point - charges is $F = k\frac{|q_1q_2|}{r^{2}}$, where $k = 9\times10^{9}\ N\cdot m^{2}/C^{2}$, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them.

Step2: Convert charges to SI units

$q_1=- 6\times10^{-6}\ C$, $q_2 = 3\times10^{-6}\ C$, and $r = 0.002\ m$.

Step3: Calculate the magnitude of the force

Substitute the values into the formula: [ \begin{align*} F&=9\times 10^{9}\frac{|(-6\times10^{-6})\times(3\times10^{-6})|}{(0.002)^{2}}\ &=9\times10^{9}\frac{| - 18\times10^{-12}|}{4\times10^{-6}}\ &=9\times10^{9}\times\frac{18\times10^{-12}}{4\times10^{-6}}\ &=\frac{9\times18\times10^{9 - 12}}{4\times10^{-6}}\ &=\frac{162\times10^{-3}}{4\times10^{-6}}\ & = 40.5\times10^{3}\ &=4.05\times10^{4}\ N\approx4\times10^{4}\ N \end{align*} ]

Step4: Determine the direction of the force

A negative charge $q_1$ and a positive charge $q_2$ attract each other. Since $q_1$ is north of $q_2$, the force on $q_2$ due to $q_1$ is in the north direction.

Answer:

magnitude: $4\times 10^{4}\ N$, direction: north