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Two charged particles 1 m apart exert a 1-N force on each other. If the magnitude of each charge is doubled, the force on each particle will be

a.1 N.
b.4 N.
c.8 N.
d.2 N.
e.none of the above

Respuesta :

Answer:2N

Explanation:

onyebuchinnaji

When the magnitude of each charge is doubled, the force on each particle will be 4N.

The given parameters;

  • distance between the two charges, r = 1 m
  • force exerted on each other by the particles, F = 1 N

The magnitude of the force exerted on the charged particles is calculated by applying Coulomb's law;

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

where;

  • F is the force of attraction or repulsion between the particles;
  • q₁ and q₂ are the magnitude of the charges
  • k is Coulomb's constant

[tex]F = \frac{k}{r^2}q_1q_2\\\\\frac{F_1}{q_1q_2} = \frac{F_2}{q_3q_4} \\\\when \ the \ charges \ are \ doubled, \ \ (q_3 = 2q_1, \ \ and \ q_4 = 2q_2)\\\\\frac{F_1}{q_1q_2} = \frac{F_2}{2q_1\times 2q_2}\\\\F_2(q_1q_2) = F_1(2q_1\times 2q_2)\\\\F_2(q_1q_2) = 4F_1(q_1q_2)\\\\F_2 = 4F_1\\\\F_2 = 4\times 1 \\\\F_2 = 4 \ N[/tex]

Thus, when the magnitude of each charge is doubled, the force on each particle will be 4N.

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