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Chapter 27: Problem 60

A circular coil with a radius of \(10.0 \mathrm{~cm}\) has 100 turns of wire and carries a current, \(i=100 . \mathrm{mA} .\) It is free to rotate in a region with a constant horizontal magnetic field given by \(\vec{B}=(0.0100 \mathrm{~T}) \hat{x}\). If the unit normal vector to the plane of the coil makes an angle of \(30.0^{\circ}\) with the horizontal, what is the magnitude of the net magnetic torque acting on the coil? 27.61 At \(t=0\) an electron crosses the positive \(y\) -axis (so \(x=0\) ) at \(60.0 \mathrm{~cm}\) from the origin with velocity \(2.00 \cdot 10^{5} \mathrm{~m} / \mathrm{s}\) in the positive \(x\) -direction. It is in a uniform magnetic field. a) Find the magnitude and the direction of the magnetic field that will cause the electron to cross the \(x\) -axis at \(x=60.0 \mathrm{~cm}\). b) What work is done on the electron during this motion? c) How long will the trip take from \(y\) -axis to \(x\) -axis?

Short Answer

Expert verified
#Answer#: To solve Part 1, follow these steps: 1. Calculate the area of the circular coil: Area = πr² = π (0.10 m)² ≈ 0.0314 m² 2. Calculate the magnetic field component in the plane of the coil: \(B_{plane} = B \times \cos{θ}\) = (5 T) × cos(30.0°) ≈ 4.33 T 3. Calculate the magnetic flux passing through the coil: Magnetic flux = n × Area × \(B_{plane}\) = 100 × 0.0314 m² × 4.33 T ≈ 13.6 Wb 4. Calculate the net magnetic torque on the coil: Torque = nABisini = (100)(0.0314 m²)(5 T)(0.1 A)sin(30.0°) ≈ 7.86 Nm The magnetic torque on the circular coil is approximately 7.86 Nm.

Step by step solution

01

Determine the magnetic torque on the circular coil

First, we need to find the area of the circular coil: Area = \(πr^2\), where r = 0.10 m Now, calculate the magnetic field component in the plane of the coil: \(B_{plane} = B \times \cos{θ}\), where θ = 30.0° After determining \(B_{plane}\), find the magnetic flux passing through the coil: Magnetic flux = \(n \times Area \times B_{plane}\), where n = 100 The net magnetic torque on the coil is determined by the formula: Torque = nABisini, B is magnetic field, i is current We already have the \(B_{plane}\), and the current i = 100 mA. Calculate the magnetic torque using the given values.

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Most popular questions from this chapter

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"?

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.

Which of the following has the largest cyclotron frequency? a) an electron with speed \(v\) in a magnetic field with magnitude \(B\) b) an electron with speed \(2 v\) in a magnetic field with magnitude \(B\) c) an electron with speed \(v / 2\) in a magnetic field with magnitude \(B\) d) an electron with speed \(2 v\) in a magnetic field with magnitude \(B / 2\) e) an electron with speed \(v / 2\) in a magnetic field with magnitude \(2 B\)

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