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blsea [12.9K]
2 years ago
10

A solenoidal coil with 22 turns of wire is wound tightly around another coil with 330 turns. The inner solenoid is 21.0 cm long

and has a diameter of 2.30 cm . At a certain time, the current in the inner solenoid is 0.140 A and is increasing at a rate of 1800 A/s .
For this time, calculate;

a) the average magnetic flux through each turn of the innersolenoid;
b) the mutual inductance of the two solenoids;
c) the emf induced in the outer solenoid by the changing current inthe inner solenoid
Thanks for any help you can offer! Explanation would be wonderful!
Physics
1 answer:
Airida [17]2 years ago
3 0

Answer:

0.00027646\ T

2.33\times 10^{-5}\ H

-0.04194 V

Explanation:

N_2 = Number of turns in outer solenoid = 330

N_1 = Number of turns in inner solenoid = 22

I_1 = Current in inner solenoid = 0.14 A

\dfrac{dI_2}{dt} = Rate of change of current = 1800 A/s

\mu_0 = Vacuum permeability = 4\pi \times 10^{-7}\ H/m

r = Radius = 0.0115 m

Magnetic field is given by

B=\mu_0\dfrac{N_2}{l}I\\\Rightarrow B=4\pi \times 10^{-7}\times \dfrac{330}{0.21}\times 0.14\\\Rightarrow B=0.00027646\ T

The  average magnetic flux through each turn of the inner solenoid is 0.00027646\ T

Magnetic flux is given by

\phi=BA\\\Rightarrow \phi=0.00027646\times \pi 0.0115^2\\\Rightarrow \phi=1.14862\times 10^{-7}\ wb

Mutual inductance is given by

M=\dfrac{N_1\phi}{I}\\\Rightarrow M=\dfrac{22\times 1.14862\times 10^{-7}}{0.14}\\\Rightarrow M=2.33\times 10^{-5}\ H

The mutual inductance of the two solenoids is 2.33\times 10^{-5}\ H

Induced emf is given by

\epsilon=-M\dfrac{dI_2}{dt}\\\Rightarrow \epsilon=-2.33\times 10^{-5}\times 1800\\\Rightarrow \epsilon=-0.04194\ V

The emf induced in the outer solenoid by the changing current inthe inner solenoid is -0.04194 V

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Answer:

The velocity of the wave is 12.5 m/s

Explanation:

The given parameters are;

he frequency of the tuning fork, f = 250 Hz

The distance between successive crests of the wave formed, λ = 5 cm = 0.05 m

The velocity of a wave, v = f × λ

Where;

f = The frequency of the wave

λ = The wavelength of the wave - The distance between crests =

Substituting the known values gives;

v =  250 Hz × 0.05 m = 12.5 m/s

The velocity of the wave, v = 12.5 m/s.

6 0
2 years ago
You stand on top a building 44 m tall with a water balloon. You drop the water balloon from rest. How fast is the balloon moving
Alecsey [184]
<h2>The balloon is moving when it is halfway down the building at 20.78 m/s.</h2>

Explanation:

We have equation of motion v² = u² + 2as

Initial velocity, u = 0 m/s  

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Displacement, s = 0.5 x 44 = 22 m

Substituting  

v² = u² + 2as

v² = 0² + 2 x 9.81 x 22

v² = 431.64

v = 20.78 m/s

Velocity at 22 m = 20.78 m/s

The balloon is moving when it is halfway down the building at 20.78 m/s.

7 0
3 years ago
Most motorcycles could win a drag race against most cars. Use<br>Newton's 2nd law to explain this.​
shutvik [7]

Answer:

is has be deducted that acceleration of an object depends only on the the mass of the object. car has a greater mass that a motorcycle.

Explanation:

the newton second law states that when a net force act on an object,the object accelerates in the direction of the net force. the acceleration is directly proportional to the net force and inversely to the mass.

mathematically, F = ma    .......................... (eqn 1)

where, F = force, m=mass and  a = acceleration

F = m(ΔV/t)    .......................... (eqn 2)

acceleration =change in velocity divide time

t = time

v= velocity

Ft = mΔV

also a∝1/m

this same second can also mean the rate of change in momentum of an object is directly proportional to the resultant force.

Drag race is a function of acceleration, therefore, a car weighs more than a motorcycle.

the reason while motorcycle moves more faster than a car is due to the weight of the motorcycle as compare to the car. if the same acceleration is applied, and there weigth are difference, this will affect the force (causing an increased resultant force for the car), whereas time used will be affected.

for example:

a motorcycle has a weight 0f 181kg

a car has a weight 0f 1590kg

from  a∝1/m

they both will moves at a different acceleration

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5 0
3 years ago
A charge of -2.65 nC is placed at the origin of an xy-coordinate system, and a charge of 2.00 nC is placed on the y axis at y =
stiks02 [169]

Answer:

A. Fnx = 5.71*10⁻⁵ N  ,  Fny= -3.67*10⁻⁵ N

B. Fn= 6.78 *10⁻⁵ N

C. α= 32.4° counterclockwise with the positive x+ axis

Explanation:

Because the particle q₃ is close to two other electrically charged particles, it will experience two electrical forces and the solution of the problem is of a vector nature.

Equivalences

1nC= 10⁻⁹C

1cm = 10⁻²m

Known data

k= 9*10⁹N*m²/C²

q₁= -2.65 nC =-2.65*10⁻⁹C

q₂= +2.00 nC = 2*10⁻⁹C

q₃= +5.00 nC= =+5*10⁻⁹C

d_{13} = \sqrt{(3.2)^{2} +(3.8)^{2} }

d_{13} =\sqrt{24.68} * 10⁻²m    = 4.9678* 10⁻²m

(d₁₃)² = 24.68*10⁻⁴m²

d₂₃ = 3.2 cm = 3.2*10⁻²m  

Graphic attached

The directions of the individual forces exerted by q₁ and q₂ on q₃ are shown in the attached figure.

The force (F₂₃) of q₂ on q₃ is repulsive because the charges have equal signs and the forces.

The force (F₁₃) of q₁ on q₃ is attractive because the charges have opposite signs.

Magnitudes of F₁₃ and F₂₃

F₁₃ = (k*q₁*q₃)/(d₁₃)²=( 9*10⁹*2.65*10⁻⁹*5*10⁻⁹) /(24.68*10⁻⁴)

F₁₃ = 4.8 *10⁻⁵ N

F₂₃ = (k*q₂*q₃)/(d₂₃)² =  ( 9*10⁹*2*10⁻⁹*5*10⁻⁹) /((3.2)²*10⁻⁴)

F₂₃ = 8.8 *10⁻⁵ N

x-y components of F₁₃ and F₂₃

F₁₃x= -4.8 *10⁻⁵ *cos β= - 4.8 *10⁻⁵(3.2/ (4.9678)= - 3.09*10⁻⁵ N

F₁₃y= -4.8 *10⁻⁵ *sin β= - 4.8 *10⁻⁵(3.8/(4.9678) =  - 3.67*10⁻⁵ N

F₂₃x  = F₂₃ =  +8.8 *10⁻⁵ N

F₂₃y = 0

x and y components of the total force exerted on q₃ by q₁ and q₂ (Fn)

Fnx= F₁₃x+F₂₃x =  - 3.09*10⁻⁵ N+8.8 *10⁻⁵ N= 5.71*10⁻⁵ N

Fny= F₁₃y+F₂₃y = - 3.67*10⁻⁵ N+0= - 3.67*10⁻⁵ N

Fn magnitude

F_{n} =\sqrt{(Fn_{x})^{2}+(Fn_{y})^{2}  }

F_{n} = \sqrt{(5.71)^{2}+(3.67)^{2}  } *10⁻⁵ N

Fn= 6.78 *10⁻⁵ N

Fn direction  (α)

\alpha =tan^{-1}( \frac{Fn_{y} }{Fn_{x} } )

\alpha =tan^{-1}( \frac{-3.67 }{5.71} )

α= -32.4°

α= 32.4° counterclockwise with the positive x+ axis

4 0
3 years ago
When will an object dropped from rest attain a speed of 30 m/s?
stich3 [128]
<h3><u>Answer</u> :</h3>

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Acceleration due to gravity = 10m/s²

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◈ <u>First equation of kinenatics</u> :

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Hence, object will attain a speed of 30m/s after 3s.

8 0
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