To solve for the charge that experiences a given force per unit charge, we need to understand the relationship between force, charge, and the electric field. The electric force [tex]\( F \)[/tex] experienced by a charge [tex]\( q \)[/tex] in an electric field [tex]\( E \)[/tex] is given by the equation:
[tex]\[ F = qE \][/tex]
This can be rearranged as:
[tex]\[ E = \frac{F}{q} \][/tex]
Given:
- The force per unit charge [tex]\((E)\)[/tex] is [tex]\(2.4 \times 6.8 \times 10^{-5} \, \text{N/C} \)[/tex].
We need to find the charge [tex]\( q \)[/tex] that will match this force per unit charge. We are provided with four potential charge values to choose from:
1. [tex]\( q_1 = 1.6 \times 10^{-7} \, \text{C} \)[/tex]
2. [tex]\( q_2 = 2.5 \times 10^{-3} \, \text{C} \)[/tex]
3. [tex]\( q_3 = 2.8 \times 10^{-3} \, \text{C} \)[/tex]
4. [tex]\( q_4 = 3.5 \times 10^1 \, \text{C} \)[/tex]
Upon matching these charge values with the given force per unit charge, we find that the correct charge value is:
[tex]\[ q_1 = 1.6 \times 10^{-7} \, \text{C} \][/tex]
Therefore, the value of the charge that experiences the given force per unit charge is [tex]\( 1.6 \times 10^{-7} \, \text{C} \)[/tex].
