1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pie
3 years ago
10

We want to construct a solenoid with a resistance of 4.30 Ω and generate a magnetic field of 3.70 × 10−2 T at its center when ap

plying 4.60 A of electrical current. We want to use copper wire with a diameter of 0.500 mm. If we need the solenoid's radius to be 1.00 cm, how many turns of wire will be need? 2 78 256 790 Then, what would be the required length of the solenoid? 12.3 cm
Physics
1 answer:
marshall27 [118]3 years ago
8 0

Answer with Explanation:

We are given that

Resistance of solenoid,R=4.3 ohm

Magnetic field,B=3.7\times 10^{-2} T

Current,I=4.6 A

Diameter of wire,d=0.5 mm=0.5\times 10^{-3} m

Radius of wire,r=\frac{d}{2}=\frac{0.5\times 10^{-3}}{2}=0.25\times 10^{-3} m

1mm=10^{-3} m

Radius of solenoid,r'=1 cm=1\times 10^{-2} m

1 cm=10^{-2} m

Resistivity of copper,\rho=1.68\times 10^{-8}\Omega m

We know that

R=\frac{\rho l}{A}

Where A=\pi r^2

Using the formula

4.3=\frac{1.68\times 10^{-8}\times l}{\pi(0.25\times 10^{-3})^2}

l=\frac{4.3\times \pi(0.25\times 10^{-3})^2}{1.68\times 10^{-8}}=50.23 m

Number of turns of wire=\frac{l}{2\pi r'}

Number of turns of wire=\frac{50.26}{2\pi(1\times 10^{-2}}=800

Hence, the number of turns of the  solenoid,N=799

Magnetic field in solenoid,B=\mu_0 nI

3.7\times 10^{-2}=4\pi\times 10^{-7} n\times 4.6

n=\frac{3.7\times 10^{-2}}{4\times 3.14\times 10^{-7}\times 4.6}

n=6404 turns/m

n=\frac{N}{L}

L=\frac{N}{n}

L=\frac{799}{6404}

L=0.125 m=0.125\times 100=12.5 cm

Length of solenoid=12.5 cm

1m=100 cm

You might be interested in
Suppose that the current in the solenoid is i(t). The self-inductance L is related to the self-induced EMF E(t) by the equation
Artemon [7]

Answer:

L =   μ₀ n r / 2I

Explanation:

This exercise we must relate several equations, let's start writing the voltage in a coil

        E_{L} = - L dI / dt

 

Let's use Faraday's law

       E = - d Ф_B / dt

in the case of the coil this voltage is the same, so we can equal the two relationships

        - d Ф_B / dt = - L dI / dt

The magnetic flux is the sum of the flux in each turn, if there are n turns in the coil

        n d Ф_B = L dI

we can remove the differentials

      n Ф_B = L I

magnetic flux is defined by

     Ф_B = B . A

in this case the direction of the magnetic field is along the coil and the normal direction to the area as well, therefore the scalar product is reduced to the algebraic product

      n B A = L I

the loop area is

      A = π R²

     

we substitute

       n B π R² = L I                    (1)

To find the magnetic field in the coil let's use Ampere's law

        ∫ B. ds = μ₀ I

where B is the magnetic field and s is the current circulation, in the coil the current circulates along the length of the coil

           s = 2π R

we solve

              B 2ππ R =  μ₀ I

              B =  μ₀ I / 2πR

we substitute in

       n ( μ₀ I / 2πR) π R² = L I

       n  μ₀ R / 2 = L I

       L =   μ₀ n r / 2I

4 0
3 years ago
If the white car experiences a change in momentum equal to 105,000 kg*m/s and is in contact with the red car for 5 seconds befor
larisa86 [58]

Answer:

21000 N

Explanation:

From the question given above, the following data were obtained:

Change in momentum = 105000 kg.m/s

Time = 5s

Force =?

Force is related to momentum and time according to the following formula:

Force = Change in momentum / time

With the above formula, we can calculate the force the white car experience during the collision. This can be obtained as illustrated below:

Change in momentum = 105000 kg.m/s

Time = 5s

Force =?

Force = Change in momentum / time

Force = 105000 / 5

Force = 21000 N

Thus, the white car experience a force of 21000 N during the collision.

4 0
3 years ago
Charge is flowing through a conductor at the rate of 420 C/min. If 742 J. of electrical energy are converted to heat in 30 s., w
Y_Kistochka [10]

Answer:

3.53 V

Explanation:

Electric charge: The is the rate of flow of electric charge along a conductor.

The S.I unit of electric charge is C.

Mathematically it is expressed as,

Q = It ............................ Equation 1

Where Q = electric charge, I = current, t = time.

I = Q/t.......................... Equation 2

From the question, charge flows through the conductor at the rate of 420 C/mim

Which means in 1 min, 420 C of charge flows through the conductor.

Hence,

Q = 420 C, t = 1 min = 60 seconds

Substitute into equation 2

I = 420/60

I =7 A

Also

P = VI......................... Equation 3

Where P = power, V = potential drop, I = current.

V = P/I................... Equation 4

Note: Power = Energy/time

From the question, P = 742/30 = 24.733 W. and I = 7 A.

Substitute these values into equation 4

V = 24.733/7

V = 3.53 V

Hence the potential drop across the conductor =  3.53 V

4 0
3 years ago
ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!
IRINA_888 [86]

Explanation:

1)5.8m/s

2)5.15m/s^2

3)12.69m/s

4)

8 0
3 years ago
"what shape are the pebble-sized particles that make up the rock?"
Fiesta28 [93]
The shape of which the pebble sized particles that makes up the rock is more of a rounded shape as they are bits and in circular formation, depicting it to be more rounder in which are particles that is made up in a rock. They can be in pebble sized or much more smaller than that when in bits.
5 0
3 years ago
Other questions:
  • A positive charge is placed in an electric field that points west. What direction is the force on the positive particle? I think
    9·1 answer
  • Jamie is writing a literary essay that examines the connection between a short story’s theme of deprivation and the author’s imp
    14·2 answers
  • What percentage of energy consumed in the united states is nonrenewable??
    15·1 answer
  • Can all rocks be weathered and eroded?how do you know?
    14·2 answers
  • When you hold a rectangular object how does the area of the side that is resting on your hand affects the pressure and the force
    6·1 answer
  • A transparent oil with index of refraction 1.28 spills on the surface of water (index of refraction 1.33), producing a maximum o
    13·1 answer
  • Three materials, put them in order of what
    6·1 answer
  • Select all the correct answers.
    5·1 answer
  • It’s 11:53pm right now and I have just this assignment left to do for this class, I need this assignment done so I don’t fail th
    6·2 answers
  • 45. When you park on a level road next to a curb: A. Your wheels must be within 18 inches of the curb B. Your front wheels must
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!