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The cockroach Periplaneta americana can detect a static electric field of magnitude 8.50 kN/C using their long antennae. If the excess static charge on a cockroach is modeled as point charges located at the end of each antenna, what magnitude of charge q would each antenna possess in order for each antennae to experience a force of magnitude 2.00 μN from the external electric field? Calculate q in units of nanocoulombs (nC) .

Respuesta :

Answer:

0.235 nC

Explanation:

Given:

  • [tex]E[/tex] = the magnitude of electric field = [tex]8.50\ kN/C =8.50\times 10^{3}\ N/C[/tex]
  • [tex]F[/tex] = the magnitude of electric force on each antenna = [tex]2.00\ \mu N =2.00\times 10^{-6}\ N[/tex]
  • [tex]q[/tex] = The magnitude of charge on each antenna

Since the electric field is the electric force applied on a charged body of unit charge.

[tex]\therefore E = \dfrac{F}{q}\\\Rightarrow q =\dfrac{F}{E}\\\Rightarrow q =\dfrac{2.00\times 10^{-6}\ N}{8.50\times 10^{3}\ N/C}\\\Rightarrow q =0.235\times 10^{-9}\ C\\\Rightarrow q =0.235\ nC[/tex]

Hence, the value of q is 0.235 nC.