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 times 107 N/C. What is the magnitude of the force on a calcium ion with charge +e? Express your answer using two significant figures.

Answer 1

Concepts and reason

The concept of electric force is required to solve the problem.

Initially, calculate the charge of the calcium ion. Finally, calculate the magnitude of the electric force by using the relation between electric field and electric force.

Fundamentals

The electric force on a charged object can be given as,

$F = qE$

Here, q is the charge and E is the electric field.

The force on a charged object is calculated by taking the product of charge on the object with the electric field value.

Since, it is given that calcium ion contains charge +e. Hence, in the expression use the value of charge as +e i.e. $1.6 \times {10^{ - 19}}{\rm{ C}}$ .

Substitute $1.6 \times {10^{ - 19}}{\rm{ C}}$ for q and $1.0 \times {10^7}{\rm{ N/C}}$ for E in the expression $F = qE$ .

$\begin{array}{c}\\F = \left( {1.6 \times {{10}^{ - 19}}{\rm{ C}}} \right)\left( {1.0 \times {{10}^7}{\rm{ N/C}}} \right)\\\\ = 1.6 \times {10^{ - 12}}{\rm{ N}}\\\end{array}$

Ans:

The force on the calcium ion is $1.6 \times {10^{ - 12}}{\rm{ N}}$ .