Two identical charged objects exert an electrostatic force of 50 N onto each other when they are 125 km apart. The force is an attractive force.

Question

What are the charges of the objects?

65.9 C each

9.3 C and -9.3 C

9.3 C each

65.9 C and -65.9 C

my choice is c

Answer 1

Coulomb's law says force is proportional to the charge of the two objects. The equation is:

F = k_eq₁q₂/r² where k_e is Coulomb's constant (8.988×10⁹ N⋅m²/C²), q₁ and q₂ are the charges of the two object (in Coulombs), and "r" is the distance between the objects.

In this case q₁ = q₂ so let's just call it "q" meaning the equation becomes:

F = k_eq²/r²

Solving for q we get: q = √(Fr²/k_e)

Remember that the distance would need to be switched to SI units. r = 125 km • 1000m/km = 125000 m

So q = √(50•125000²/8.988×10⁹) = √86.926 = 9.3 Coulombs. Since this is an attractive force, one charge is positive and the other negative (answer b)