To determine the value of the charge that creates the given electric potential at a specified distance, we can use the formula for the electric potential [tex]\( V \)[/tex] due to a point charge:
[tex]\[ V = \frac{1}{4 \pi \epsilon_0} \cdot \frac{q}{r} \][/tex]
Where:
- [tex]\( V \)[/tex] is the electric potential.
- [tex]\( \epsilon_0 \)[/tex] is the permittivity of free space ([tex]\( 8.854187817 \times 10^{-12} \)[/tex] F/m).
- [tex]\( q \)[/tex] is the charge.
- [tex]\( r \)[/tex] is the distance from the charge.
Given:
- The electric potential [tex]\( V = 580 \)[/tex] V.
- The distance [tex]\( r = 1.34 \)[/tex] m.
We need to find the charge [tex]\( q \)[/tex]. Rearranging the formula to solve for [tex]\( q \)[/tex]:
[tex]\[ q = V \cdot r \cdot 4 \pi \epsilon_0 \][/tex]
Given values can be substituted to find [tex]\( q \)[/tex].
After performing the calculations as described step-by-step, we get the result:
[tex]\[ q \approx 8.647516235042814 \times 10^{-8} \text{ C} \][/tex]
To express the charge in terms of [tex]\( \times 10^{-8} \)[/tex] C, we can write:
[tex]\[ q \approx 8.647516235042813 \][/tex]
Thus, the value of the charge, considering it should include the sign and in terms of [tex]\( \times 10^{-8} \)[/tex] C is:
[tex]\[ \boxed{8.647516235042813} \][/tex]
