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Chapter 19: Problem 74

A solenoid has 4850 turns per meter and radius \(3.3 \mathrm{cm}\) The magnetic field inside has magnitude 0.24 T. What is the current in the solenoid?

Short Answer

Expert verified
Answer: The current flowing through the solenoid is approximately 3.11 A.

Step by step solution

01

Write down the given values and the formula for the magnetic field inside a solenoid.

The given values are number of turns per meter (\(n = 4850 \, turns/m\)), radius (\(r = 3.3 \, cm\)), and the magnetic field inside the solenoid (\(B = 0.24 \, T\)). The permeability of free space (\(\mu_0 = 4\pi \times 10^{-7} \, Tm/A\)) is a constant value. We will use Ampère's law: $$ B = \mu_0 \cdot n \cdot I $$
02

Solve the formula for current I.

We want to find the current I in the solenoid. Therefore, rearrange the formula to get I by itself: $$ I = \frac{B}{\mu_0 \cdot n} $$
03

Plug in the given values and solve for I.

Now, we can substitute the given values into the formula and calculate the current I: $$ I = \frac{0.24 T}{(4\pi \times 10^{-7} \, Tm/A)(4850 \, turns/m)} $$ After plugging in the numbers and doing the calculations, we get: $$ I \approx 3.11 A $$ So the current in the solenoid is approximately 3.11 A.

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Most popular questions from this chapter

In Problem \(35,\) the width of the strip is \(3.5 \mathrm{cm},\) the magnetic field is \(0.43 \mathrm{T}\), the Hall voltage is measured to be $7.2 \mu \mathrm{V},\( the thickness of the strip is \)0.24 \mathrm{mm},$ and the current in the wire is 54 A. What is the density of carriers (number of carriers per unit volume) in the strip?
In an electric motor, a coil with 100 turns of radius \(2.0 \mathrm{cm}\) can rotate between the poles of a magnet. The magnetic field strength is $0.20 \mathrm{T}\(. When the current through the coil is \)50.0 \mathrm{mA},$ what is the maximum torque that the motor can deliver?
Prove that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of its speed. (This is the principle on which the cyclotron operates.) In doing so, write an expression that gives the period \(T\) (the time for one revolution) in terms of the mass of the particle, the charge of the particle, and the magnetic field strength.
A solenoid of length \(0.256 \mathrm{m}\) and radius \(2.0 \mathrm{cm}\) has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of \(4.5 \mathrm{A}\) in the wire?
Two identical bar magnets lic next to one another on a table. Sketch the magnetic ficld lines if the north poles are at the same end.
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