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You remove two socks from a hot dryer and find that they repel with forces of 0.00400 N when they’re 2.00 cm apart. If they have equal charges, how much charge does each sock have?

Respuesta :

cjrodriguez89

Answer:

13.4*10⁻⁹ C = 13.4 nC

Explanation:

  • Assuming  we can treat both socks as point charges, the repulsive force between them, must obey Coulomb's Law, as follows:

       [tex]F = \frac{k*Q^{2} }{d^{2}} = 4e-3 N[/tex]

  • where k = 9*10⁹ N*m²/C², d= 0.02 m.
  • Replacing these values in the above equation, we can solve for  Q, as we know that both socks have equal charges, as follows:
  • [tex]Q = \sqrt{\frac{d^{2}*F}{k}} = \sqrt{\frac{(0.02m)^{2}*4.3e-3N}{9e9 N*m2/C2}}\\ \\ Q= 13.4e-9C = 13.4 nC[/tex]
Cricetus

Each soak have "13.4 nC" charges. A further explanation is provided in the below segment.

According to the question,

Force,

  • F = 0.004 N

Distance,

  • d = 2.00 cm

We know,

  • k = [tex]9\times 10^9 \ Nm^2/C^2[/tex]

By applying Coulomb's law, we get

→ [tex]F = \frac{k\times Q^2}{d^2}[/tex]

or,

→ [tex]Q = \sqrt{\frac{d^2\times F}{k} }[/tex]

By substituting the values, we get

      [tex]= \sqrt{\frac{(0.02)^2\times 4.3e-3}{9\times 10^9} }[/tex]

      [tex]= 13.4 e-9[/tex]

      [tex]= 13.4 \ nC[/tex]

Thus the above answer is right.

Learn more:

https://brainly.com/question/14668407

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