Answer to Question #92367 in Electricity and Magnetism for Alabi temitope

Question

Three charges Q1
= -2μC (0,0)cm, Q2
= 4 μC (0,10)cm
and Q3
= -3 μC (15,0)cm acts on one another. Find the
magnitude of the total electric force and the angle
that the total electric force makes with the positive
x-axis.

Answer 1

The total electric force is given by formula:

$F_{net} = \sqrt {{F_{x}}^2+{F_{y}}^2} (1)$

Coulomb law

$F= k×\frac {q_{1}×q_{2}}{r^2} (2)$

where k=9×10⁹

Using (2) we get

Fx= 2.4 N (3)

Fy=7.2 N (4)

We put (3) and (4) in (1)

F=7.59 N

$\tanθ=\frac {F_{y}}{F_{x}} (5)$

We put (3) and (4) in (5)

$\tanθ=3$

θ=252°

The angle is equal to

360°-252°=108°

Answer

7.59 N

108°