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Chapter 23: Problem 3

What would be the consequence of setting the potential at \(+100 \mathrm{~V}\) at infinity, rather than taking it to be zero there? a) Nothing; the field and the potential would have the same values at every finite point. b) The electric potential would become infinite at every finite point, and the electric field could not be defined. c) The electric potential everywhere would be \(100 \mathrm{~V}\) higher, and the electric field would be the same. d) It would depend on the situation. For example, the potential due to a positive point charge would drop off more slowly with distance, so the magnitude of the electric field would be less.

Short Answer

Expert verified
Answer: The consequence of setting the electric potential at infinity to +100 V is that the electric potential at every finite point will be 100 V higher, while the electric field remains the same.

Step by step solution

01

Checking option a)

The first option proposes that changing the potential at infinity to +100 V would have no effect on the electric field or potential at every finite point. This looks contradictory, since the potential is directly related to the electric field, so it can't remain unaffected when the reference point is changed. Therefore, option a) is not correct.
02

Checking option b)

The second option suggests that if we set the potential at infinity to +100 V, the electric potential would become infinite at every finite point, and the electric field could not be defined. This statement seems unrealistic because the electric field would still exist, in spite of changing the reference point of the potential. Thus, option b) is not correct either.
03

Checking option c)

The third option says that changing the potential at infinity would cause the electric potential everywhere to be 100 V higher, while the electric field would remain the same. Indeed, setting the potential to +100 V at infinity would shift the reference point, but this shift will not alter the electric field since it only depends on the position of charges and their magnitudes. Consequently, option c) seems the most logical, and we accept option c) as the correct answer.
04

Checking option d) for understanding

The last option suggests that the result of setting the potential at infinity to +100V would depend on the situation. However, this is not the case, as it will only shift the reference point without affecting the electric field. Therefore, option d) is incorrect. In conclusion, modifying the reference point for potential at infinity to +100 V only affects the potential's value by adding 100 V everywhere, while the electric field remains unchanged. Therefore, the correct answer is option c).

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Most popular questions from this chapter

The electric potential energy of a continuous charge distribution can be found in a way similar to that used for systems of point charges in Section \(23.6,\) by breaking the distribution up into suitable pieces. Find the electric potential energy of an arbitrary spherically symmetrical charge distribution, \(\rho(r) .\) Do not assume that \(\rho(r)\) represents a point charge, that it is constant, that it is piecewise-constant, or that it does or does not end at any finite radius, \(r\). Your expression must cover all possibilities. Your expression may include an integral or integrals that cannot be evaluated without knowing the specific form of \(\rho(r) .\) (Hint: A spherical pearl is built up of thin layers of nacre added one by one.)

The electron beam emitted by an electron gun is controlled (steered) with two sets of parallel conducting plates: a horizontal set to control the vertical motion of the beam, and a vertical set to control the horizontal motion of the beam. The beam is emitted with an initial velocity of \(2.00 \cdot 10^{7} \mathrm{~m} / \mathrm{s}\). The width of the plates is \(d=5.00 \mathrm{~cm}\), the separation between the plates is \(D=4.00 \mathrm{~cm},\) and the distance between the edge of the plates and a target screen is \(L=40.0 \mathrm{~cm}\) In the absence of any applied voltage, the electron beam hits the origin of the \(x y\) -coordinate system on the observation screen. What voltages need to be applied to the two sets of plates for the electron beam to hit a target placed on the observation screen at coordinates \((x, y)=(0 \mathrm{~cm}, 8.00 \mathrm{~cm}) ?\)

Two fixed point charges are on the \(x\) -axis. A charge of \(-3.00 \mathrm{mC}\) is located at \(x=+2.00 \mathrm{~m}\) and a charge of \(+5.00 \mathrm{mC}\) is located at \(x=-4.00 \mathrm{~m}\) a) Find the electric potential, \(V(x),\) for an arbitrary point on the \(x\) -axis. b) At what position(s) on the \(x\) -axis is \(V(x)=0 ?\) c) Find \(E(x)\) for an arbitrary point on the \(x\) -axis.

A point charge of \(+2.0 \mu C\) is located at \((2.5 \mathrm{~m}, 3.2 \mathrm{~m})\) A second point charge of \(-3.1 \mu \mathrm{C}\) is located at \((-2.1 \mathrm{~m}, 1.0 \mathrm{~m})\). a) What is the electric potential at the origin? b) Along a line passing through both point charges, at what point(s) is (are) the electric potential(s) equal to zero?

Two point charges are located at two corners of a rectangle, as shown in the figure. a) What is the electric potential at point \(A ?\) b) What is the potential difference between points \(A\) and \(B ?\)
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