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Chapter 9: Problem 33

Two oppositely charged parallel plates are held apart at distance of \(10 \mathrm{~cm}\). The potential difference between them is maintained at 50 volts. The electric field between them is (A) \(5 \mathrm{~V} / \mathrm{m}\), down (B) \(50 \mathrm{~V} / \mathrm{m}\), up (C) \(500 \mathrm{~V} / \mathrm{m}\), down (D) \(500 \mathrm{~V} / \mathrm{m}\), up (E) \(1 / 50 \mathrm{~V} / \mathrm{m}\), down

Short Answer

Expert verified
Answer: The electric field between the plates is 500 V/m.

Step by step solution

01

In this scenario, the relationship between electric field (E), potential difference (V), and distance (d) can be described by the following formula: \(E = \frac{V}{d}\) Where E is the electric field, V is the potential difference, and d is the distance between the two plates. #Step 2: Convert the distance to meters#

The distance between the plates is given in centimeters. To properly use the formula, we need the distance in meters. Convert 10 cm to meters: \(d = 10 \mathrm{~cm} \times \frac{1 \mathrm{~m}}{100 \mathrm{~cm}} = 0.1 \mathrm{~m}\) #Step 3: Calculate the electric field#
02

Using the given potential difference of 50 V and the converted distance of 0.1 meters, apply the formula to find the electric field: \(E = \frac{V}{d} = \frac{50 \mathrm{~V}}{0.1 \mathrm{~m}} = 500 \mathrm{~V} / \mathrm{m}\) #Step 4: Determine the direction of the electric field#

Since the plates are oppositely charged, we can deduce that the electric field will be directed from the positively charged plate to the negatively charged plate. The exercise does not specifically state which plate is positively or negatively charged. Therefore, it is impossible to determine whether the direction of the electric field is up or down. Using the calculated electric field, the closest option in the list given is: (C) \(500 \mathrm{~V} / \mathrm{m}\), down However, without the information on the charge of the plates, we cannot confirm whether the direction is indeed down or up.

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Most popular questions from this chapter

A circular loop rotates around a horizontal axis coming out of the page (side view shown, below). The loop is rotating in a uniform \(B\)-field, pointed downward. For every two full rotations, how often does the induced current change direction? (A) Twice (B) Four times (C) Eight times (D) Twelve time (E) Sixteen times

An electron is released from rest just above a very large, negatively charged sheet, which carries surface charge density \(\sigma=5 \mathrm{nC} / \mathrm{m}^2\). When the electron is \(0.5 \mathrm{~m}\) above the sheet its speed is most nearly (A) \(4 \times 10^8 \mathrm{~m} / \mathrm{s}\) (B) \(3 \times 10^8 \mathrm{~m} / \mathrm{s}\) (C) \(5 \times 10^7 \mathrm{~m} / \mathrm{s}\) (D) \(1 \times 10^7 \mathrm{~m} / \mathrm{s}\) (E) \(300 \mathrm{~m} / \mathrm{s}\)

Two identical conducting spheres, \(A\) and \(B\) carry charges \(+Q\) and \(-Q\), respectively. A third, identical conducting sphere \(C\) carries charge \(Q=0\). Sphere \(A\) is touched to sphere \(C\) and separated. Next, sphere \(B\) is touched to sphere \(C\) and separated. Finally, \(A\) is touched to \(B\) and separated. What is the final charge on each sphere? (A) \(A=Q ; B=-Q ; C=0\) (B) \(A=Q / 2 ; B=Q / 2 ; C=Q / 4\) (C) \(A=Q / 8 ; B=Q / 8 ; C=-Q / 4\) (D) \(A=Q / 2 ; B=-Q / 4 ; C=-Q / 4\) (E) \(A=Q / 4 ; B=-Q / 8 ; C=-Q / 4\)

The sign of \(q\) remains positive and the sign of \(2 q\) is changed to negative. Is there any point along the \(x\)-axis where the electric field could be zero? (A) Yes, somewhere to the left of the charge marked \(q\) (B) Yes, somewhere to the right of the charge marked \(2 q\) (C) Yes, between the two charges but closer to \(q\) (D) Yes, between the two charges but closer to \(2 q\) (E) No, the field can never be zero

Metal sphere \(A\) has a radius of \(5 \mathrm{~cm}\) and metal sphere \(B\) has a radius of \(10 \mathrm{~cm}\). Sphere \(A\) carries a charge of \(9 \mathrm{nC}\) and sphere \(B\) carries a charge of \(18 \mathrm{nC}\). If the surfaces of \(A\) and \(B\) are \(185 \mathrm{~cm}\) apart, the potential energy between them is (A) \(7.29 \times 10^{-17} \mathrm{~J}\) (B) \(7.88 \times 10^{-9} \mathrm{~J}\) (C) \(7.88 \times 10^{-7} \mathrm{~J}\) (D) \(7.29 \times 10^{-9} \mathrm{~J}\) (E) None of the above
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