What is the Motional EMF in a Solenoid with a Square Loop Inside?

In summary, a square wire loop is placed inside a solenoid with a circular cross section. The solenoid is 16.0 cm long with 95 turns of wire and a current of 3.00 A. The flux through the loop can be found by multiplying the magnetic field inside the solenoid (B=(μo)(I)(N/l)) by the area of the square loop. If the current is reduced to zero in 4.00 s, the average induced EMF in the loop can be found using the formula EMF = -N x mflux / delta t.
  • #1
goWlfpack
51
0

Homework Statement



A square, single-turn wire loop 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius 3.00 cm, as shown in the figure below. The solenoid is 16.0 cm long and wound with 95 turns of wire.

(a) If the current in the solenoid is 3.00 A, find the flux through the loop.
T · m2

(b) If the current in the solenoid is reduced to zero in 4.00 s, find the magnitude of the average induced emf in the loop.
V



Homework Equations



EMF=-N mflux/delta t

where N is the number of turns

The Attempt at a Solution


im just having trouble manipulating the equation to get my unknowns...
 
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  • #2
First things first: What's the field inside the solenoid?
 
  • #3
given as B=constant(current)/2R
radius is 3 so
6.3e-7?
 
  • #4
You'd better look up the formula for the field within a solenoid.
 
  • #5
Doc Al said:
You'd better look up the formula for the field within a solenoid.

ok i found the magnetic field inside the solenoid. it is B=(Moconstant)(I)(N/l)
where N is the number of turns and l is the length
this comes to .00224
so then i tried to multiply it by the area of the soleniod and i got the wrong answer.
so i tried it multiplied by the area of the square loop inside the soleniod and that was also a red x...
any help?
 
  • #6
goWlfpack said:
ok i found the magnetic field inside the solenoid. it is B=(Moconstant)(I)(N/l)
where N is the number of turns and l is the length
this comes to .00224
Looks OK.
so then i tried to multiply it by the area of the soleniod and i got the wrong answer.
That was a mistake, since you need the flux through the square loop.
so i tried it multiplied by the area of the square loop inside the soleniod and that was also a red x...
That should work. Is the loop oriented perpendicular to the field or is it at some other angle? What did you use for the area of the loop?
 
  • #7
Doc Al said:
Looks OK.

That was a mistake, since you need the flux through the square loop.

That should work. Is the loop oriented perpendicular to the field or is it at some other angle? What did you use for the area of the loop?

yea sorry minor mathmatical error. I got it now! thanks for all the help! :)
 

FAQ: What is the Motional EMF in a Solenoid with a Square Loop Inside?

What is a motional emf solenoid problem?

A motional emf solenoid problem is a physics problem in which a solenoid (a coil of wire) is moving through a magnetic field, causing an induced emf (electromotive force) in the wire. This phenomenon is known as motional emf and is caused by the magnetic field interacting with the moving charges in the wire.

How do you calculate the induced emf in a motional emf solenoid problem?

The induced emf in a motional emf solenoid problem can be calculated using the equation E = -N * (dΦ/dt), where N is the number of turns in the solenoid and dΦ/dt is the rate of change of the magnetic flux through the solenoid. This equation is known as Faraday's law of induction.

What factors affect the induced emf in a motional emf solenoid problem?

The induced emf in a motional emf solenoid problem is affected by several factors, including the strength of the magnetic field, the velocity of the solenoid, and the number of turns in the solenoid. The direction of the induced emf also depends on the direction of the magnetic field and the velocity of the solenoid.

How is a motional emf solenoid problem different from a regular solenoid?

A regular solenoid is a static coil of wire that creates a uniform magnetic field when a current is passed through it. In a motional emf solenoid problem, the solenoid is moving through a magnetic field, causing an induced emf in the wire. This means that the magnetic field is not constant and the induced emf is time-dependent.

Why is a motional emf solenoid problem important in physics?

Motional emf solenoid problems are important in physics because they demonstrate the principles of electromagnetic induction and the relationship between magnetic fields and electric fields. They also have practical applications in devices such as generators and motors, where the motion of a wire through a magnetic field can be used to generate electricity or produce mechanical motion.

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