Question

PLEASE HELP I’LL MARK YOU BRAINLIEST!!!!

Answer 1

Answer: Net electrostatic force on C is 24.2×$10^{-2}$ Newtons.

Explanation: Coulomb's Law is used to determine Electrostatic Force. Its formula is:

F = k.$\frac{q_{0}.q_{1}}{r^{2}}$

where:

k is electrostatic constant (k = 8.987×$10^{9}$ Nm²/C²);

q is the charge of the object in Coulumb;

r is the distance between charges;

The net force is the sum of all the forces acting on C, so:

Force B on C:

They are both positive, so there is a relpusive force acting between them on the y-axis.

$F_{BC} = 8,987.10^{9}.\frac{4.35.10^{-3}.9.67.10^{-4}}{(6.14.10^{2})^{2}}$

$F_{BC} = 10.03.10^{-2}$ N

Force D on C:

There is an atractive force between them on the x-axis.

$F_{CD} = 8.987.10^{9}.\frac{9.67.10^{-4}.1.92.10^{-3}}{(1.42.10^{3})^{2}}$

$F_{CD} = 13.64.10^{-4}$ N

Force A on C:

First, find the distance between objects:

The distance is a diagonal line that divides the rectangle into a right triangle. Distance is square of the hypotenuse .

$r^{2} = (6.14.10^2)^{2} + (1.42.10^{3})^{2}$

$r^{2} = 37.72.10^{4}$

and hypotenuse: r = $6.14.10^2$m

There is an atractive force between charges, but there are components of the force in x- and y-axis. So, because of that, force will be:

$F_{CA} = F_{CA}$.sinα + $F_{CA}.$cosα

$F_{CA} = 8.987.10^{9}.\frac{3.12.10^{-3}.9.67.10^{-4}}{37.72.10^{4}}$

$F_{CA} = 7.2.10^{-2}$

The trigonometric relations is taken from the rectangle:

sinα = $\frac{6.14.10^{2}}{6.14.10^{2}}$

cosα = $\frac{1.42.10^{3}}{6.14.10^{2}}$

$F_{CA}.$cosα = $7.2.10^{-2}(\frac{1.42.10^{3}}{6.14.10^{2}})$ = 0.17

$F_{CA}.$sinα = $7.2.10^{-2}.(\frac{6.14.10^{2}}{6.14.10^{2}} )$ = 0.072

$F_{CA} =$ 0.17î + 0.072^j

Now, sum up all the terms in its respective axis:

X: $13.64.10^{-4} + 0.17 =$ 0.1714

Y: $10.03.10^{-2} + 7.2.10^{-2}$ = 0.1723

These forms another right triangle, whose hypotenuse is the net electrostatic force:

$F_{net} = \sqrt{(0.1714)^{2} + (0.1723)^2}$

$F_{net} = 24.3.10^{-2}$ N

The net electrostatic force acting on C has magnitude $F_{net} = 24.3.10^{-2}$ N.