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A fixed system of charges exerts a force of magnitude 21 N on a 6 C charge. The 6 C charge is replaced with a 8 C charge. What is the exact magnitude of the force (in N) exerted by the system of charges on the 8 C charge?

Respuesta :

meerkat18
According to the gravitational force law, force existing between two objects is proportional to the mass of the two objects and inversely proportional to the square of the distance between them. when 8 C charge is replaced by 6 C charge without changing the distance, then the force is

21/6 = F/8
 F = 28 N 

Answer: The correct answer is 28 Newtons.

Explanation:

To calculate the force exerted by the system having charges, we use the formula given by Coulomb's Law, which is:

[tex]F=\frac{kq_1q_2}{r^2}[/tex]

where, k = constant

[tex]q_1\text{ and }q_2[/tex] = two charges

r = distance between the two charges.

  • The force when one charge is 6 C:

[tex]21=\frac{kq_1\times 6}{r^2}[/tex]     ...(1)

  • The force when one charge is 8 C:

[tex]F=\frac{kq_1\times 8}{r^2}[/tex]     ...(2)

Taking the ratios of 2 and 1, we get:

[tex]\frac{F}{21}=\left(\frac{\frac{kq_1\times 8}{r^2}}{\frac{kq_1\times 6}{r^2}}\right)\\\\F=\frac{8\times 21}{6}\\\\F=28N[/tex]

Hence, the correct answer is 28 Newtons.

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