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
Vladimir79 [104]
3 years ago
5

g A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to th

e plane of the coil makes an angle of 30.0° with the direction of the field. When the magnetic field is increased from 250 µT to 700 µT in 0.300 s, an emf of magnitude 60.0 mV is induced in the coil. What is the total length of wire in the coil?
Physics
1 answer:
abruzzese [7]3 years ago
4 0

Answer:

L = 182.4 m      

Explanation:

Given:-

- The number of turns of the coil, N = 50

- The shape of the coil = square

- The angle between the coil and magnetic field, θ = 30°

- The change in magnetic field, ΔB = ( 700 - 250 ) μT

- The time duration in which magnetic field changes, Δt = 0.3 s

- The induced emf, E = 60.0 mV

Solution:-

- The problem at hand is an application of Faraday's law. The law states that the induced emf ( E ) is proportional to the negative rate of change of magnetic flux ( ΔФ / Δt ) and number of turns of the coil ( N ).

- The Faraday's law is mathematically expressed as:

                    E =  - N* ( ΔФ / Δt )

Where,

- The flux ( Ф ) through a current carrying with an cross-sectional area ( A ) at a normal angle ( θ ) to the direction of magnetic field ( B ) is given by the following relationship.

                    Ф = B*A*cos ( θ )

- We need the rate of change of magnetic flux ( ΔФ / Δt ) for the Faraday's law. I.e the induced emf ( E ) is proportional to rate of change in magnetic field ( ΔB / Δt ), rate of change of angle between the coil and magnetic field ( Δθ / Δt ) or rate of change of cross-sectional area of the coil under the influence of magnetic field.

- To determine the exact relationship. We will derive the multi-variable function of flux ( Ф ) with respect to time "t":

                     Ф ( B , A , θ ) = B*A*cos ( θ )

- The first derivative would be ( Use chain and product rules )

    ( ΔФ / Δt ) = ΔB / Δt*A*cos ( θ ) + B*ΔA/Δt*cos ( θ ) - B*A*sin ( θ )*Δθ/Δt

- For the given problem the only dependent parameter that is changing is magnetic field ( B ) with respect to time "t". Hence, ( ΔA/Δt = Δθ/Δt = 0 ):

                        ΔФ / Δt  = (ΔB/Δt)*A*cos ( θ )

- Substitute the rate of change of magnetic flux  ( ΔФ / Δt ) into the expression for Faraday's Law initially stated:

                        E =  - N*(ΔB/Δt)*A*cos ( θ )

- Plug in the values and evaluate the Area of the square coil:

                       A =  - E / ( N*(ΔB/Δt)*cos ( θ ) )

                       A = - 0.06 / ( 50*[ (250-700)*10^-6/0.3 ] *cos ( 30° ) )

                       A = - 0.06 / -0.07216

                       A = 0.8314 m^2

- The square coil has equal sides ( x ). The area of a square A is given by:

                      A = x^2

                      x = √0.8314

                      x = 0.912 m

 

- The perimeter length of a single coil in terms of side length "x" is given as:

                      P = 4x

Whereas for a coil of N turns the total length ( L ) would be:

                      L = N*P

                      L = 4Nx

                      L = 4 * 50 * 0.912

                      L = 182.4 m                 ... Answer

You might be interested in
Bare free charges do not remain stationary when close together. To illustrate this, calculate the acceleration of two isolated p
Marta_Voda [28]

Answer:

Acceleration, a=9.91\times 10^{15}\ m/s^2

Explanation:

It is given that,

Separation between the protons, r=3.73\ nm=3.73\times 10^{-9}\ m

Charge on protons, q=1.6\times 10^{-19}\ C

Mass of protons, m=1.67\times 10^{-27}\ kg

We need to find the acceleration of two isolated protons. It can be calculated by equating electric force between protons and force due to motion as :

ma=\dfrac{kq^2}{r^2}

a=\dfrac{kq^2}{mr^2}      

a=\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{1.67\times 10^{-27}\times (3.73\times 10^{-9})^2}      

a=9.91\times 10^{15}\ m/s^2

So, the acceleration of two isolated protons is 9.91\times 10^{15}\ m/s^2. Hence, this is the required solution.

3 0
3 years ago
Two particles, one with charge -5.45 × 10^-6 C and one with charge 4.39 × 10^-6 C, are 0.0209 meters apart. What is the magnitud
Levart [38]

Explanation:

Given that,

Charge 1, q_1=-5.45\times 10^{-6}\ C

Charge 2, q_2=4.39\times 10^{-6}\ C

Distance between charges, r = 0.0209 m

1. The electric force is given by :

F=k\dfrac{q_1q_2}{r^2}

F=9\times 10^9\times \dfrac{-5.45\times 10^{-6}\times 4.39\times 10^{-6}}{(0.0209)^2}

F = -492.95 N

2. Distance between two identical charges, r=0.0209\ m

Electric force is given by :

F=\dfrac{kq_3^2}{r^2}

q_3=\sqrt{\dfrac{Fr^2}{k}}

q_3=\sqrt{\dfrac{492.95\times (0.0209)^2}{9\times 10^9}}

q_3=4.89\times 10^{-6}\ C

Hence, this is the required solution.

3 0
3 years ago
Jonathan has six strings that are the same thickness and are all the same material. He cuts the strings to different lengths and
harkovskaia [24]
The shortest string will have the highest pitch.

7 0
3 years ago
Read 2 more answers
A dog has a weight of 700N find the mass of the dog
Stolb23 [73]
The specific answer for that will be 71.38 kg
8 0
3 years ago
On which of the temperature scales does water boil at the highest numerical value? A. Celsius B. Fahrenheit C. Kelvin D. Latent
velikii [3]
Answer is C. Kelvin, Kelvin is the temperature scales does water boil at the highest numerical value. Hope it helped you, and have a great day.

-Charlie
7 0
3 years ago
Read 2 more answers
Other questions:
  • Calculate the gravitational potential energy a 1kg ball has when thrown 3 m into the air. The gravitational field strength on ea
    10·1 answer
  • The gravity model predicts that the optimal location of a service is
    15·1 answer
  • Hooke's law describes a certain light spring of unstretched length 33.6 cm. when one end is attached to the top of a doorframe a
    7·1 answer
  • What happens when heat from inside Earth is transferred to its surface? A:Warmer material is pushed to the crust B:More dense ma
    9·2 answers
  • A is the area of a chromosome pair that attaches to a fiber stretching
    9·1 answer
  • A stationary block resting on the ground is pulled up with a tension force of 100N, but does not leave the ground.
    5·1 answer
  • What are some non examples of proton
    13·1 answer
  • Which correctly lists three main causes of deforestation?
    8·2 answers
  • PLEASE HELP THIS IS A 53 QUESTION TEST
    13·1 answer
  • A train moving west with an initial velocity of 20 m/s accelerates at 4 m/s2 for 10 seconds. During this tim
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!