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Chapter 23: Problem 4

In which situation is the electric potential the highest? a) at a point \(1 \mathrm{~m}\) from a point charge of \(1 \mathrm{C}\) b) at a point \(1 \mathrm{~m}\) from the center of a uniformly charged spherical shell of radius \(0.5 \mathrm{~m}\) with a total charge of \(1 \mathrm{C}\) c) at a point \(1 \mathrm{~m}\) from the center of a uniformly charged rod of length \(1 \mathrm{~m}\) and with a total charge of \(1 \mathrm{C}\) d) at a point \(2 \mathrm{~m}\) from a point charge of \(2 \mathrm{C}\) e) at a point \(0.5 \mathrm{~m}\) from a point charge of \(0.5 \mathrm{C}\)

Short Answer

Expert verified
Answer: All situations have the same electric potential.

Step by step solution

01

Situation A: Point Charge of \(1 \mathrm{C}\)

In this case, we have a point charge of \(1\mathrm{C}\), and the distance from the charge is \(1\mathrm{~m}\). Using the formula for electric potential, \(V_A = \frac{k(1\mathrm{C})}{1\mathrm{~m}} = k\).
02

Situation B: Uniformly Charged Spherical Shell

In this situation, we have a uniformly charged spherical shell with a total charge of \(1\mathrm{C}\) and the distance from the center is \(1\mathrm{~m}\). Since the shell is uniformly charged, we can also use the formula for electric potential, considering the total charge \(Q\). Thus, \(V_B = \frac{k(1\mathrm{C})}{1\mathrm{~m}} = k\).
03

Situation C: Uniformly Charged Rod

For the uniformly charged rod, we can approximate the electric potential at the point \(1\mathrm{~m}\) from the center of the rod (as it is a uniformly charged rod with a length of \(1\mathrm{~m}\)) by using the point charge formula with total charge \(Q\). So, \(V_C= \frac{k(1\mathrm{C})}{1\mathrm{~m}} = k\).
04

Situation D: Point Charge of \(2 \mathrm{C}\)

In this situation, we have a point charge of \(2\mathrm{C}\), and the distance from the charge is \(2\mathrm{~m}\). Using the formula for electric potential, \(V_D =\frac{k(2\mathrm{C})}{2\mathrm{~m}} = k\).
05

Situation E: Point Charge of \(0.5 \mathrm{C}\)

In this case, we have a point charge of \(0.5\mathrm{C}\), and the distance from the charge is \(0.5\mathrm{~m}\). Using the formula for electric potential, \(V_E = \frac{k(0.5\mathrm{C})}{0.5\mathrm{~m}} = k\). Now, let's compare the electric potentials. We have: \(V_A = k\) ; \(V_B = k\) ; \(V_C = k\) ; \(V_D = k\) ; \(V_E = k\). All the electric potentials are equal to k. Therefore, there is no situation in which the electric potential is the highest, as they are all the same.

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