Question

The figure shows five electric charges. Four charges with the magnitude of the charge 2.0 nC form a square with the size a = 4.0 cm . Positive charge with the magnitude of q = 5.5 nC is placed in the center of the square.
A) What is the magnitude of the force on the 5.5 nC charge in the middle of the figure due to the four other charges?

B) What is the direction of the force on the 5.5 nC charge in the middle of the figure due to the four other charges?

Answer 1

Considering the four electric charges forming a square with magnitude of charge of 2.0 nC on each. :

A) Magnitude of the force on the 5.5 nC charge in the middle of the figure = 3.48 * 10^-4 N

B) Direction of the force on the 5.5 nC charge in the middle of the figure = Leftward ( negative x -axis )

Using the given data :

size of square = 4 cm

magnitudes of four charges = 2.0 nC

a) magnitude of the force on the center charge

Electric force between two point charges = $F = \frac{1}{4\pi *E_{o} } \frac{q1q2}{r^2}$ ----- ( 1 )

where ; $\frac{1}{4\pi E_{o} } = 9 * 10^9 Nm^2/C^2$

step 1 ; find r ( distance between charges )

r² = ( 2 )² + ( 2 )² = 8 cm²  

back to equation 1

F = 9 * 10⁹ * $\frac{2 * 10^{-9} * (5.5 * 10^{-9}) }{8*10^{-4} }$ =  1.23 * 10^-4  N

∴ magnitude of the force on the center charge ( Fnet )= 4F cos 45°

        = 4 * ( 1.23 * 10^-4 ) * $\frac{1}{\sqrt{2} }$  = 3.48 * 10^-4 N

b) The direction of the force at the center is along the negative x-axis ( leftward )

Learn more : brainly.com/question/24139734