Question

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 ???? would each antenna possess in order for each antennae to experience a force of magnitude 5.50 μN from the external electric field? Calculate ???? in units of nanocoulombs (nC) .

Answer 1

Answer:

0.647 nC

Explanation:

The force experienced by a charge due to the presence of an electric field is given by

$F=qE$

where

q is the charge

E is the magnitude of the electric field

In this problem, each antenna is modelled as it was a single point charge, experiencing a force of

$F=5.50\mu N = 5.50\cdot 10^{-6} N$

Therefore, if the electric field magnitude is

$E=8.50 kN/C = 8500 N/C$

Then the charge on each antenna would be

$q=\frac{F}{E}=\frac{5.50\cdot 10^{-6} N}{8500 N/C}=6.47\cdot 10^{-10} C = 0.647 nC$