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Chapter 27: Problem 12

A proton, moving in negative \(y\) -direction in a magnetic field, experiences a force of magnitude \(F\), acting in the negative \(x\) -direction. a) What is the direction of the magnetic field producing this force? b) Does your answer change if the word "proton" in the statement is replaced by “electron"?

Short Answer

Expert verified
Answer: The direction of the magnetic field is in the negative \(z\)-direction. b) Would the result change if we considered an electron moving the same way as a proton? Answer: No, the result would not change. The direction of the magnetic field would still be in the negative \(z\)-direction for an electron.

Step by step solution

01

Identify given information

We are given that the force has a magnitude \(F\) and acts in the negative \(x\)-direction. Also, the proton is moving in the negative \(y\)-direction.
02

Apply the right-hand rule

From the formula mentioned earlier, \(\vec{F} = q(\vec{v} \times \vec{B})\), we can use the right-hand rule to determine the direction of the magnetic field. Point your right hand's thumb in the direction of the proton's velocity, which is the negative \(y\)-direction. Since the proton is positively charged, curl your fingers in the direction of the force, which is the negative \(x\)-direction. The direction your palm faces now will be the direction of the magnetic field.
03

Find the direction of the magnetic field

In this case, your palm will be facing downwards, which means the magnetic field is in the negative \(z\)-direction. a) So, the direction of the magnetic field is in the negative \(z\)-direction.
04

Consider the case of an electron

Now, let's see if the result changes if we replace the proton with an electron. The only difference is that an electron has a negative charge, so using the left-hand rule instead of the right-hand rule for negatively charged particles, we follow the same process as in steps 2 and 3. b) In this case, you will find that the magnetic field is still in the negative \(z\)-direction. So, the answer does not change whether we consider a proton or an electron. The direction of the magnetic field in both cases is in the negative \(z\)-direction.

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Most popular questions from this chapter

A proton moving with a speed of \(4.0 \cdot 10^{5} \mathrm{~m} / \mathrm{s}\) in the positive \(y\) -direction enters a uniform magnetic field of \(0.40 \mathrm{~T}\) pointing in the positive \(x\) -direction. Calculate the magnitude of the force on the proton.

A straight wire carrying a current of 3.41 A is placed at an angle of \(10.0^{\circ}\) to the horizontal between the pole tips of a magnet producing a field of \(0.220 \mathrm{~T}\) upward. The poles tips each have a \(10.0 \mathrm{~cm}\) diameter. The magnetic force causes the wire to move out of the space between the poles. What is the magnitude of that force?

A proton is accelerated from rest by a potential difference of \(400 .\) V. The proton enters a uniform magnetic field and follows a circular path of radius \(20.0 \mathrm{~cm} .\) Determine the magnitude of the magnetic field.

A 30 -turn square coil with a mass of \(0.250 \mathrm{~kg}\) and a side length of \(0.200 \mathrm{~m}\) is hinged along a horizontal side and carries a 5.00 -A current. It is placed in a magnetic field pointing vertically downward and having a magnitude of \(0.00500 \mathrm{~T}\). Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. Use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).

In the Hall effect, a potential difference produced across a conductor of finite thickness in a magnetic field by a current flowing through the conductor is given by a) the product of the density of electrons, the charge of an electron, and the conductor's thickness divided by the product of the magnitudes of the current and the magnetic field. b) the reciprocal of the expression described in part (a). c) the product of the charge on an electron and the conductor's thickness divided by the product of the density of electrons and the magnitudes of the current and the magnetic field. d) the reciprocal of the expression described in (c). e) none of the above.
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