Question

A protein molecule in an electrophoresis gel has a negative charge.The exact charge depends on the pH of the solution, but 30 excesselectrons is typical. What is the magnitude of the electric forceon a protein with this charge in a 1500 N/C electric field?

Answer 1

Concepts and reason

The concept of electric force experienced by a charge placed in electric field is required to solve this problem.

Initially, find the charge on given number of electrons. Then, write the expression of the electric force and then substitute the values.

Fundamentals

The force experienced by a charge $q$ placed in an electric field is,

$F = qE$

Here, $F$ is the force experienced by the charge placed in electric field $E$.

The expression for the total charge $q$ on $n$ number of electrons is,

$q = ne$

Here,$n$ is the number of electrons and $e$ is the electric charge.

The total charge on electrons is given by following expression:

$q = ne$

Substitute $1.6 \times {10^{ - 19}}{\rm{ C}}$ for $e$ and $30$ for $n$ as follows:

$\begin{array}{c}\\q = ne\\\\ = \left( {30} \right)\left( {1.6 \times {{10}^{ - 19}}{\rm{ C}}} \right)\\\\ = 4.8 \times {10^{ - 18}}{\rm{ C}}\\\end{array}$

The force experienced by a charge $q$ placed in an electric field is,

$F = qE$

Substitute $4.8 \times {10^{ - 18}}{\rm{ C}}$ for $q$ and $1500{\rm{ N/C}}$ for $E$ as follows:

$\begin{array}{c}\\F = qE\\\\ = \left( {4.8 \times {{10}^{ - 18}}{\rm{ C}}} \right)\left( {1500{\rm{ N/C}}} \right)\\\\ = 7.2 \times {10^{ - 15}}{\rm{ C}}\\\end{array}$

Ans:

The magnitude of the electric force on the protein is $7.2 \times {10^{ - 15}}{\rm{ C}}$.