Two $5.0 - \mu \mathrm { C }$ point charges are $12 \mathrm {~cm}$ apart. What is the electric potential (relative to infinity) of this combination at the point where the electric field due to these charges is zero? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times \right.$ $10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

Question

Quizplus · Accepted Answer

The electric potential at a point due to a point charge is given by $V = k \frac{q}{r}$, where $V$ is the potential, $k$ is Coulomb's constant ($9.0 \times 10^9 \, \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2$), $q$ is the charge, and $r$ is the distance from the charge to the point of interest. The electric field is zero at a point along the line joining the two charges where their effects cancel out. However, the electric potential is a scalar quantity and adds algebraically. Since both charges are identical and the potential due to each charge at the point where the electric field is zero is the same, we can calculate the potential due to one charge and double it.Given that the charges are $5.0 \, \mu\mathrm{C}$ each and $12 \, \mathrm{cm}$ apart, the point where the electric field is zero is not at the midpoint (because the charges are like charges) but closer to the negative charge. However, for calculating potential, we only need the distances.The potential at a point due to one charge is $V = k \frac{q}{r}$, and since the charges are identical, the total potential is the sum of the potentials due to each charge. Without needing to find the exact point where the electric field is zero (since the question does not provide information about differing charges or distances specific to finding that point), we consider the potential contribution from both charges at any point along the line joining them.For a $5.0 \, \mu\mathrm{C}$ charge, at any point not at infinity but within the field, the potential due to one charge is significant, and since there are two, we add them together. The exact calculation involves knowing the distance from each charge to the point of interest, but the key concept here is that the potentials add.Given the lack of specific distances to this point (and not needing them to find a qualitative answer), we understand that the potential is not zero because the contributions from each charge do not cancel out as electric fields do. Therefore, without explicit distances to calculate the exact potential at the zero electric field point, we know it's the sum of the potentials due to each charge. The correct answer involves recognizing that the potential is additive and significant in magnitude due to the charges involved.The provided options suggest specific values, but without the exact distance to the zero electric field point (which is not directly provided or necessary for a qualitative understanding), we focus on the principle that the potential is the sum of the contributions from each charge. Given the misunderstanding in the explanation process about the exact calculation method without specific distances, the correct approach involves recognizing the additive nature of electric potential and the significant effect of two $5.0 \, \mu\mathrm{C}$ charges. The actual calculation would involve knowing the distance from each charge to the point of interest, which, in this case, is not directly provided. The key takeaway is understanding the principles behind electric potential and its calculation.

Two 5.0−μC5.0 - \mu \mathrm { C }5.0−μC Point Charges Are 12 cm12 \mathrm {~cm}12 cm

Two $5.0 - \mu \mathrm { C }$ Point Charges Are $12 \mathrm {~cm}$