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

0.647 nC

Step-by-step 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=(F)/(E)=(5.50\cdot 10^(-6) N)/(8500 N/C)=6.47\cdot 10^(-10) C = 0.647 nC`