A) Charge q1 = +5.60 nC is on the x-axis at x = 0 and an unknown charge q2 is on the x-axis at x = -4.00 cm. The total electric force that q1 and q2 exert on a third charge q3 = +2.00 nC on the x -axis at x = 4.00 cm is in the +x-direction and has magnitude 49.0 μN. Find the x-component of the force that q1 exerts on q3. b) Find the x-component of the force that q2 exerts on q3.

c) Find the charge q2

a) F₃₁ = 63.0 μN  

b) F₃₂ = - 14.0 μN

c) q₂ = - 5.0 nC

Explanation:

a)

Assuming that the three charges can be taken as point charges, the forces between them must obey Coulomb's Law, and can be found independent each other, applying the superposition principle.So, we can find the force that q₁ exerts along the x-axis on q₃, as follows:

       

b)

Since total force exerted by q₁ and q₂ on q₃ is 49.0 μN, we can find the force exerted only by q₂ (which is along the x-axis only too) just by difference, as follows:

     

c)

Finally, in order to find the value of q₂, as we know the value and sign of F₃₂, we can apply again the Coulomb's Law, solving for q₂, as follows:

     

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