Question

Large electric fields in cell membranes cause ions to move through the cell wall. The field strength in a typical membrane is 1.0 x 10 7 N/C. What is the magnitude of the force on a calcium ion with charge +e? What is its acceleration?Is it possible for a particle with the same charge as as calcium to have a different acceleration if placed at this location?What would change the acceleration: mass of the particle? diameter of the particle?

Answer 1

1) Magnitude of the force: $1.6\cdot 10^{-12} N$

The magnitude of the electric force on an electric charge is:

$F=qE$

where q is the charge and E the electric field. In this problem:

$q = +e = +1.6\cdot 10^{-19} C$ is the charge of the calcium ion

$E=1.0 \cdot 10^7 N/C$ is the magnitude of the electric field

Substituting,

$F=(1.6\cdot 10^{-19}C)(1.0\cdot 10^7 N/C)=1.6\cdot 10^{-12} N$

2) Acceleration: $2.5\cdot 10^{13} m/s^2$

The atomic mass of a calcium ion is approx. 40 a.m.u, this means that its mass is

$m=40 \cdot (1.6\cdot 10^{-27}kg)=6.4\cdot 10^{-26} kg$

And so, the acceleration of the ion is given by Newton's second law:

$a=\frac{F}{m}=\frac{1.6\cdot 10^{-12}N}{6.4\cdot 10^{-26} kg}=2.5\cdot 10^{13} m/s^2$

3) Yes

Explanation: a particle with same charge (+e) of the calcium ion could have the same acceleration of the calcium ion if it has exactly the same mass. In fact, the acceleration depends only on two factors: the mass and the force, so it both are the same, than the acceleration does not change.

4) The mass of the particle

In fact, the acceleration of the particle is given by:

$a=\frac{F}{m}$

where F is the electric force and m the mass. Therefore, if the mass changes ,the acceleration changes as well.