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Chapter 9: Problem 2

Two conducting spheres of differing radii are in contact, as shown. A positively charged rod is touched to the large sphere and removed to a great distance. The large and small spheres are then separated. We can then say that (A) the big sphere will be positively charged and the smaller sphere will be negatively charged. (B) both spheres will be positively charged. (C) the big sphere will be negatively charged and the smaller sphere will be positively charged. (D) both spheres will be negatively charged. (E) all the charge will migrate to the smaller sphere.

Short Answer

Expert verified
Answer: (B) Both spheres will be positively charged.

Step by step solution

01

Understand charge balance

In this problem, we will first touch a positively charged rod to the larger sphere. Since both spheres are conductors, when the charged rod touches the larger sphere, excess positive charges will distribute evenly on the surfaces of both spheres.
02

Relationship between charges and radii

It's important to note that the charge on the spheres will distribute according to the radii of the spheres. Here, we must understand that a larger sphere has more surface area than a smaller sphere. Consequently, the larger sphere can accommodate more charges than the smaller sphere.
03

Choose the correct option

Considering the behavior in Step 1 and the relationship between the sphere sizes discussed in Step 2, both spheres will be positively charged when the charged rod is touched to the larger sphere. So, the correct answer is (B) both spheres will be positively charged.

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Most popular questions from this chapter

The positively charged rod is brought near the large sphere, but without touching it. The two spheres are separated and lastly the rod removed to a distance. We can then say that (A) the big sphere will be positively charged and the smaller sphere will be negatively charged. (B) both spheres will be positively charged. (C) the big sphere will be negatively charged and the smaller sphere will be positively charged. (D) both spheres will be negatively charged. (E) all the charge will migrate to the smaller sphere.

A proton is launched from a very long negatively charged plate at an initial velocity \(v_o\) and angle \(\theta\) toward an identical, positively charged plate, as shown below. The two plates are held at a potential difference \(V=1000\) volts, and the distance between the two plates is \(d\). a) Draw in the electric field vectors. Write an algebraic expression for the electric field strength in terms of given quantities. b) If \(v_o=4 \times 10^5 \mathrm{~m} / \mathrm{s}\), and \(\theta=60^{\circ}\), does \(--_{-}--_{-}--_{-}--^{-}\) the proton hit the top plate? If so, with what velocity? c) If \(d=25 \mathrm{~cm}\), how long is the proton in flight? d) If a uniform magnetic field pointing along the proton's initial velocity vector is introduced between the plates, does this alter the conclusion to (b)?

A rectangular loop is situated in a region with a uniform magnetic field of \(0.1 \mathrm{~T}\) pointing into the page, as shown below. The length of the loop is \(20 \mathrm{~cm}\) and the width is \(10 \mathrm{~cm}\). a) What is the magnetic flux through the loop? b) If the value of \(B\) is increased from \(0.1 \mathrm{~T}\) to \(0.5 \mathrm{~T}\) in \(0.3 \mathrm{~s}\), what will be the EMF induced into the loop? What will be the direction of the induced current? Justify your answer. c) If the resistance of the loop is \(R=1 \Omega\), what is the value of the current? d) If the \(B\)-field is tilted at an angle \(\theta=15^{\circ}\) from the normal to the page, what is the flux through the loop? e) Give two ways that one could change the induced EMF in the loop, other than changing \(B\). f) Draw a rotation axis from left to right in the plane of the page that passes through the loop's center. The loop is rotated about this axis at a constant angular velocity. Write an expression for the flux in terms of the angular velocity \(\omega\) and the time \(t\).

Two identical point charges \(q_1\) and \(q_2\) are at a distance \(r\) apart. If the size of \(q_1\) is doubled and the distance between them tripled, the strength of the electrical force between them (A) goes up by a factor of 3 . (B) goes down by a factor of 3 . (C) goes down by a factor of 9 . (D) goes down by a factor of \(2 / 3\). (E) goes down by a factor of \(2 / 9\)

What potential difference between the two plates would be needed to accelerate a hydrogen ion (a proton) from rest to a speed of \(10^6 \mathrm{~m} / \mathrm{s}\) ? (A) \(100 \mathrm{~V}\) (B) \(500 \mathrm{~V}\) (C) \(1000 \mathrm{~V}\) (D) \(5000 \mathrm{~V}\) (E) \(10,000 \mathrm{~V}\)
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