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
Mamont248 [21]
3 years ago
8

Three parallel wires of length l each carry current Iin the same direction. They’re positioned at the vertices of an equilateral

triangle of side a, and oriented perpendicular to the triangle.
Find an expression for the magnitude of the force on each wire.

Express your answer in terms of the variables I, l, a, and appropriate constants.
Physics
2 answers:
cluponka [151]3 years ago
6 0

Answer:

F = μi²l/πa

Explanation:

The magnetic force F on a length of wire, l carrying a current i in a magnetic field B is given by

F = Bilsinθ      

The magnetic field due to one wire of length, l carrying a current, i at a distance a from it is given by B = μi/2πa

So, the force on the first wire due to the second wire is F₁ = Bilsinθ = μiilsinθ/2πa = μi²lsinθ/2πa

the force on the first wire due to the third wire is F₂ = Bilsinθ = μiilsinθ/2πa = μi²lsinθ/2πa

Since the magnetic field due to the one wire is perpendicular to the length of the other wire its field acts upon, θ = 90

So, F₁ = μi²lsinθ/2πa = μi²lsin90/2πa = μi²l/2πa and

F₂ = μi²lsinθ/2πa = μi²lsin90/2πa = μi²l/2πa

Since the angle between F₁ and F₂ is 60° (since it is an equilateral triangle)

The resultant force F is thus

F = √(F₁² + F₂² + 2F₁F₂cos60°)

F = √(F₁² + F₂² + 2F₁F₂ × 0.5)

F = √(F₁² + F₂² + 2F₁F₂)   (since F₁ = F₂)

F = √(2F₁² + 2F₁²) = √(4F₁²)

F = 2F₁

F = 2μi²l/2πa

F = μi²l/πa

Free_Kalibri [48]3 years ago
5 0

Answer:

F_{1}=\frac{\mu _{0}I_{1}I_{2}}{2\pi a}l+\frac{\mu _{0}I_{1}I_{3}}{2\pi a}l=\frac{\mu _{0}I_{1}}{2\pi a}l(I_{2}+I_{3})

Explanation:

To solve this problem we can use the expression for the force between two wires with currents I1 and I2, at a distance of r.

F_{1}=F_{2}=\frac{\mu _{0}I_{1}I_{2}}{2\pi r}L

where L is the length of the wires. Wires feel the same force and the currents are in the same direction.

For our problem the three wires the force is the same. By taking into account that the distance among them is <em>a</em> we have

F_{1}=F_{2}=F_{3}

and the force on on of the wire is the sum of the effects of the others

F_{1}=\frac{\mu _{0}I_{1}I_{2}}{2\pi a}l+\frac{\mu _{0}I_{1}I_{3}}{2\pi a}l=\frac{\mu _{0}I_{1}}{2\pi a}l(I_{2}+I_{3})

where we have taken <em>r=a</em> (wires are equidistant in a equilateral triangle)and <em>L=l </em>for our problem

I hope this is useful for you

regards

You might be interested in
Ivan drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Ivan drove h
lesya692 [45]

Answer:252 miles

Explanation:

Given

During his way to mountain it took 7 hr to drive

and during his return trip it took 4 hr to return

Let x be the distance between home and mountain

average speed for return is  27 miles per hour faster than his former trip

let v be the speed on his way to mountain thus v+27 is his return speed

thus 7=\frac{x}{v}----1

for return trip

4=\frac{x}{v+27}-----2

divide  1 & 2

\frac{7}{4}=\frac{x\cdot (v+27)}{v\cdot x}

7v=4v+4\cdot 27

3v=4\cdot 27

v=36 mph

thus x=7\times 36=252\ miles

7 0
3 years ago
What would be the orbital speed and period of a satellite in orbit 0.82 ✕ 108 m above the earth?
Ivenika [448]
The answer should be 88.56
3 0
3 years ago
A 6.0 m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40
MrRissso [65]

Answer:

a) t = 0.0185 s = 18.5 ms

b) T = 874.8 N

Explanation:

a)

First we find the seed of wave:

v = fλ

where,

v = speed of wave

f = frequency = 810 Hz

λ = wavelength = 0.4 m

Therefore,

v = (810 Hz)(0.4 m)

v = 324 m/s

Now,

v = L/t

where,

L = length of wire = 6 m

t = time taken by wave to travel length of wire

Therefore,

324 m/s = 6 m/t

t = (6 m)/(324 m/s)

<u>t = 0.0185 s = 18.5 ms</u>

<u></u>

b)

From the formula of fundamental frquency, we know that:

Fundamental Frequency = v/2L = (1/2L)(√T/μ)

v = √(T/μ)

where,

T = tension in string

μ = linear mass density of wire = m/L = 0.05 kg/6 m = 8.33 x 10⁻³ k gm⁻¹

Therefore,

324 m/s = √(T/8.33 x 10⁻³ k gm⁻¹)

(324 m/s)² = T/8.33 x 10⁻³ k gm⁻¹

<u>T = 874.8 N</u>

8 0
3 years ago
A gray kangaroo can bound across level ground with each jump carrying it 9.1 m from the takeoff point. Typically the kangaroo le
Alona [7]

Answer:

u = 10.63 m/s

h = 1.10 m

Explanation:

For Take-off speed ..

by using the standard range equation we have

R = u² sin2θ/g

R = 9.1 m

θ = 26º,

Initial velocity = u

solving for u

u² = \frac{Rg}{sin2\theta}

u^2 = \frac{9.1 x 9.80}{sin26}

u^2 = 113.17

u = 10.63 m/s

for Max height

using the standard h(max) equation ..

v^2 = (v_osin\theta)^2 -2gh

h =\frac{(v_o^2sin\theta)^2}{2g}

h  =  \frac{(113.17)(sin26)^2}{(2 x 9.80)}}

h = 1.10 m

7 0
3 years ago
reasons. 5. Why is the unit of temperature called a fundamental unit? Give reasons. ring derived unit.​
Furkat [3]

Explanation:

It doesn't depends upon other.

It have it's own identity.

It's a lot easier to measure temperature than to measure the motion of component particles.

8 0
3 years ago
Other questions:
  • Which two conditions would result in the weakest electric force between objects?
    11·1 answer
  • A guitar string has a linear density of 8.30 ✕ 10−4 kg/m and a length of 0.660 m. the tension in the string is 56.7 n. when the
    5·2 answers
  • The ___of a wave is the number of wavelengths that pass a fixed point in a second.
    7·1 answer
  • What makes an atom an ion?
    7·1 answer
  • An iron wire and a copper wire of the same length have the same potential difference applied to them. What must be the ratio of
    10·1 answer
  • Elements in the family often have a similar
    6·2 answers
  • All of the following are electromagnetic waves except
    15·1 answer
  • Rubber is a type of _________.<br> radiator<br> distributor<br> insulator<br> conductor
    11·2 answers
  • (04.02 LC)
    13·2 answers
  • How is gravity involved while swinging?<br>​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!