Answer :
To find the charge, we can use the formula that relates the electric field [tex]\( E \)[/tex] to a point charge [tex]\( q \)[/tex]:
[tex]\[ E = \frac{k \cdot |q|}{r^2} \][/tex]
Where:
- [tex]\( E \)[/tex] is the electric field, which is [tex]\( 59.1 \, \text{N/C} \)[/tex].
- [tex]\( k \)[/tex] is the Coulomb constant, [tex]\( 8.98755 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/tex].
- [tex]\( r \)[/tex] is the distance from the charge, [tex]\( 48.4 \, \text{m} \)[/tex].
- [tex]\( |q| \)[/tex] is the magnitude of the charge.
The formula can be rearranged to solve for the charge [tex]\( q \)[/tex]:
[tex]\[ |q| = \frac{E \cdot r^2}{k} \][/tex]
Let's plug in the values:
1. Square the distance [tex]\( r \)[/tex]:
[tex]\[ r^2 = (48.4)^2 \][/tex]
2. Multiply the electric field [tex]\( E \)[/tex] by [tex]\( r^2 \)[/tex]:
[tex]\[ E \cdot r^2 = 59.1 \cdot (48.4)^2 \][/tex]
3. Divide by the Coulomb constant [tex]\( k \)[/tex] to find [tex]\( |q| \)[/tex]:
[tex]\[ |q| = \frac{59.1 \cdot (48.4)^2}{8.98755 \times 10^9} \][/tex]
After calculating these steps, the magnitude of the charge is approximately:
[tex]\[ |q| = 1.5404119698916835 \times 10^{-5} \, \text{C} \][/tex]
So, the charge is approximately [tex]\( 1.54 \times 10^{-5} \, \text{C} \)[/tex].
[tex]\[ E = \frac{k \cdot |q|}{r^2} \][/tex]
Where:
- [tex]\( E \)[/tex] is the electric field, which is [tex]\( 59.1 \, \text{N/C} \)[/tex].
- [tex]\( k \)[/tex] is the Coulomb constant, [tex]\( 8.98755 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)[/tex].
- [tex]\( r \)[/tex] is the distance from the charge, [tex]\( 48.4 \, \text{m} \)[/tex].
- [tex]\( |q| \)[/tex] is the magnitude of the charge.
The formula can be rearranged to solve for the charge [tex]\( q \)[/tex]:
[tex]\[ |q| = \frac{E \cdot r^2}{k} \][/tex]
Let's plug in the values:
1. Square the distance [tex]\( r \)[/tex]:
[tex]\[ r^2 = (48.4)^2 \][/tex]
2. Multiply the electric field [tex]\( E \)[/tex] by [tex]\( r^2 \)[/tex]:
[tex]\[ E \cdot r^2 = 59.1 \cdot (48.4)^2 \][/tex]
3. Divide by the Coulomb constant [tex]\( k \)[/tex] to find [tex]\( |q| \)[/tex]:
[tex]\[ |q| = \frac{59.1 \cdot (48.4)^2}{8.98755 \times 10^9} \][/tex]
After calculating these steps, the magnitude of the charge is approximately:
[tex]\[ |q| = 1.5404119698916835 \times 10^{-5} \, \text{C} \][/tex]
So, the charge is approximately [tex]\( 1.54 \times 10^{-5} \, \text{C} \)[/tex].
