Answer
To calculate the strength of the electric force needed to generate a force field, use Coulomb's Law:
\[
F = k \frac{|q_1 q_2|}{r^2}
\]
Where:
- \( F \) is the electric force,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the charges,
- \( r \) is the distance between the charges.
Measure the charges and distance, plug the values into the formula, and solve for \( F \) to find the required electric force strength.
Solution
To calculate the strength of the electric force needed to generate a force field, we need to consider the following known conditions and principles:
1. **Coulomb's Law**: The electric force \( F \) between two charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by the formula:
\[
F = k \frac{|q_1 q_2|}{r^2}
\]
where \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \).
2. **Electric Field Strength**: The electric field \( E \) created by a charge \( q \) at a distance \( r \) is given by:
\[
E = k \frac{|q|}{r^2}
\]
3. **Force on a Charge in an Electric Field**: The force \( F \) experienced by a charge \( q_0 \) in an electric field \( E \) is given by:
\[
F = q_0 E
\]
### Steps to Calculate the Electric Force Strength
1. **Identify the Charges**: Determine the values of the charges \( q_1 \) and \( q_2 \) that will create the force field.
2. **Determine the Distance**: Measure or define the distance \( r \) between the charges.
3. **Calculate the Electric Field**: Use the electric field formula to find the strength of the electric field \( E \) generated by one of the charges at the location of the other charge.
4. **Calculate the Force**: If you have a specific charge \( q_0 \) that will experience the force in the electric field, use the force formula to find the electric force \( F \).
### Example Calculation
Let's say we have a charge \( q_1 = 1 \, \text{C} \) and we want to calculate the electric force on a charge \( q_0 = 1 \, \text{C} \) at a distance \( r = 1 \, \text{m} \).
1. **Calculate the Electric Field**:
\[
E = k \frac{|q_1|}{r^2} = 8.99 \times 10^9 \frac{1}{1^2} = 8.99 \times 10^9 \, \text{N/C}
\]
2. **Calculate the Force**:
\[
F = q_0 E = 1 \times 8.99 \times 10^9 = 8.99 \times 10^9 \, \text{N}
\]
Thus, the strength of the electric force needed to generate the force field in this example is \( 8.99 \times 10^9 \, \text{N} \).
If you have specific values for the charges and distance, please provide them, and I can perform the calculations accordingly.
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
