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Delvig [45]
3 years ago
11

(a) A long, straight solenoid has N turns, uniform cross-sectional area A, and length l. Show that the inductance of this soleno

id is given by the equation L=μ0AN2/l. Assume that the magnetic field is uniform inside the solenoid and zero outside. (Your answer is approximate because B is actually smaller at the ends than at the center. For this reason, your answer is actually an upper limit on the inductance.) (b) A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils. If you connect such a spring in an electric circuit, how much self-inductance must you include for it if you model it as an ideal solenoid?
Physics
1 answer:
Paul [167]3 years ago
6 0

Answer:

a. L = μ₀AN²/l b. 1.11 × 10⁻⁷ H

Explanation:

a. The magnetic flux through the solenoid, Ф = NAB where N = number of turns of solenoid, A = cross-sectional area of solenoid and B = magnetic field at center of solenoid = μ₀ni where μ₀ = permeability of free space, n = number of turns per unit length = N/l where l = length of solenoid and i = current in solenoid.

Also, Li = Ф where L = inductance of solenoid.

So, Li = NAB

= NA(μ₀ni)

= NA(μ₀Ni/l)

Li = μ₀AN²i/l

dividing both sides by i, we have

So, L = μ₀AN²/l

b. The self- inductance, L = μ₀AN²/l where

A = πd²/4 where d = diameter of solenoid = 0.150 cm = 1.5 × 10⁻³ m, N = 50 turns, μ₀ = 4π × 10⁻⁷ H/m and l = 5.00 cm = 5 × 10⁻² m

So, L = μ₀AN²/l

L = μ₀πd²N²/4l

L = 4π × 10⁻⁷ H/m × π(1.5 × 10⁻³ m)²(50)²/(4 × 5 × 10⁻² m)

L = 11,103.3 × 10⁻¹¹ H

L = 1.11033 × 10⁻⁷ H

L ≅ 1.11 × 10⁻⁷ H

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Answer:

See explanation

Explanation:

Solution:-

Electric current produces a magnetic field. This magnetic field can be visualized as a pattern of circular field lines surrounding a wire. One way to explore the direction of a magnetic field is with a compass, as shown by a long straight current-carrying wire in. Hall probes can determine the magnitude of the field. Another version of the right hand rule emerges from this exploration and is valid for any current segment—point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it.

Compasses placed near a long straight current-carrying wire indicate that field lines form circular loops centered on the wire. Right hand rule 2 states that, if the right hand thumb points in the direction of the current, the fingers curl in the direction of the field. This rule is consistent with the field mapped for the long straight wire and is valid for any current segment.

( See attachments )

- The equation for the magnetic field strength - B - (magnitude) produced by a long straight current-carrying wire is given by the Biot Savart Law:

                                  B = \frac{uo*I}{2\pi *r}

Where,

I : The current,

r : The shortest distance to the wire,

uo : The permeability of free space. = 4π * 10^-7  T. m/A

-  Since the wire is very long, the magnitude of the field depends only on distance from the wire r, not on position along the wire. This is one of the simplest cases to calculate the magnetic field strength - B - from a current.

- The magnetic field of a long straight wire has more implications than one might first suspect. Each segment of current produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each segment. The formal statement of the direction and magnitude of the field due to each segment is called the Biot-Savart law. Integral calculus is needed to sum the field for an arbitrary shape current. The Biot-Savart law is written in its complete form as:

                             B = \frac{uo*I}{4\pi }*\int\frac{dl xr}{r^2}      

Where the integral sums over,

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3 0
3 years ago
Why is the nucleus of an atom dense​
Inessa [10]

Explanation:

The nucleus of an atom is dense because it contains more of particles in a very little space.

The nucleus is the center of an atom made up of the protons and neutrons.

Atomic nucleus is very small compared to the size of the atom.

 Density is function of mass and volume.

Mass is the amount of matter in a substance.

Volume is the space occupied by a substance.

    The more the mass the more the density.

Since protons and neutron are massive bodies occupying a small space, they make the nucleus very dense.

learn more:

Density brainly.com/question/5055270

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7 0
3 years ago
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galben [10]

Answer:

\triangle P=1.95*10^{-4}

Explanation:

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Generally the equation for Friction factor is mathematically given by

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Generally the equation for Friction factor is mathematically given by

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3 years ago
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son4ous [18]

Answer:

Explanation:

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v_new = 3v.

Note: the mass of the school does not change it is constant

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K.E_new = ½m × 9v²

K.E_new = 9 × ½mv²

Since K.E = ½mv²

Then,

K.E_new = 9 × K.E

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D. It will be nine times greater.

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3 years ago
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UNO [17]

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the number of neutrons and protons in an atom

6 0
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