Explore a diverse range of topics and get expert answers on IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.
Sagot :
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]
[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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.