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Chapter 20: Problem 75

A uniform magnetic field of magnitude 0.29 T makes an angle of \(13^{\circ}\) with the plane of a circular loop of wire. The loop has radius $1.85 \mathrm{cm} .$ What is the magnetic flux through the loop?

Short Answer

Expert verified
Question: Calculate the magnetic flux through a circular loop of wire with a radius of 1.85 cm, placed in a uniform magnetic field of 0.29 T. The angle between the magnetic field and the plane of the loop is 13°. Answer: The magnetic flux through the circular loop is approximately 0.000307 Tm².

Step by step solution

01

1. Calculate the area of the circular loop

The area A of the circular loop can be calculated using the formula A = πr². We are given the radius r = 0.0185 m, so: A = π(0.0185)² A ≈ 0.001076 m²
02

2. Convert the angle to radians

The angle θ is given in degrees, we need to convert it to radians first: θ = 13° × (π/180) θ ≈ 0.227 radians
03

3. Calculate the magnetic flux through the loop

Now we can calculate the magnetic flux Φ using the formula: Φ = B × A × cos(θ) Φ = (0.29 T) × (0.001076 m²) × cos(0.227 radians) Φ ≈ 0.000307 Tm² So, the magnetic flux through the circular loop is approximately 0.000307 Tm².

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Most popular questions from this chapter

An airplane is flying due north at \(180 \mathrm{m} / \mathrm{s}\). Earth's magnetic field has a northward component of \(0.30 \mathrm{mT}\) and an upward component of \(0.38 \mathrm{mT}\). (a) If the wingspan (distance between the wingtips) is \(46 \mathrm{m},\) what is the motional emf between the wingtips? (b) Which wingtip is positively charged?
A solenoid is \(8.5 \mathrm{cm}\) long, \(1.6 \mathrm{cm}\) in diameter, and has 350 turns. When the current through the solenoid is \(65 \mathrm{mA},\) what is the magnetic flux through one turn of the solenoid?
A doorbell uses a transformer to deliver an amplitude of \(8.5 \mathrm{V}\) when it is connected to a \(170-\mathrm{V}\) amplitude line. If there are 50 turns on the secondary, (a) what is the turns ratio? (b) How many turns does the primary have?
An ideal inductor of inductance \(L\) is connected to an ac power supply, which provides an emf \(\mathscr{E}(t)=\mathscr{E}_{\mathrm{m}}\) sin \(\omega t\) (a) Write an expression for the current in the inductor as a function of time. [Hint: See Eq. \((20-7) .]\) (b) What is the ratio of the maximum emf to the maximum current? This ratio is called the reactance. (c) Do the maximum emf and maximum current occur at the same time? If not, how much time separates them?
The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude \(16 \mathrm{V}\). What is the emf amplitude in the secondary? (tutorial: transformer)
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