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If you secure a refrigerator magnet about 2mmfrom the metallic surface of a refrigerator door and then move the magnet sideways, you can feel a resistive force, indicating the presence of eddy currents in the surface.

A)Estimate the magnetic field strength Bof the magnet to be 5 mTand assume the magnet is rectangular with dimensions 4 cmwide by 2 cmhigh, so its area A is 8 cm2. Now estimate the magnetic flux ΦB into the refrigerator door behind the magnet.
Express your answer with the appropriate units.

B)If you move the magnet sideways at a speed of 2 cm/s, what is a corresponding estimate of the time rate at which the magnetic flux through an area A fixed on the refrigerator is changing as the magnet passes over? Use this estimate to estimate the emf induced under the rectangle on the door's surface.
Express your answer with the appropriate units.

Respuesta :

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Answer:

(A) 4* 6 ^ ⁻6 T m² (B) 2 * 10 ^ ⁻6 v

Explanation:

Solution

Given that:

A refrigerator magnet about = 2 mm

The estimated magnetic field strength of the magnet is = 5 m T

The Area = 8 cm²

Now,

(A) The magnetic flux ΦB = BA

Thus,

ΦB  = (5 * 10^⁻ 3) ( 4 * 10 ^⁻2) * ( 2 * 10^ ⁻2) Tm²

So,

ΦB =  4* 6 ^ ⁻6 T m²

(B)By applying Faraday's Law we have the following formula given below:

Ε = Bℓυ

Here,

ℓ = 2 cm the same as 2 * 10 ^⁻2 m

B = 5 m T = 5 * 10 ^ ⁻3 T

υ = 2 cm/s  = 2 * 10 ^ ⁻2 m/s

Thus,

Ε = (5 * 10 ^ ⁻3 T) *  (2 * 10 ^ ⁻2) (2 * 10 ^ ⁻2) v

E =2 * 10 ^ ⁻6 v

batolisis

A) The magnetic flux ΦB into the refrigerator door behind the magnet :

  • 4 * 6⁻⁶ Tm²

B) The estimated emf induced under the rectangle on the door's surface ;

  • 2 * 10⁻⁶ v

Given data :

magnetic field strength of magnet ( B )  = 5 mT

size of refrigerator magnet = 2 mm

Area of magnet ( A )  = 4 * 2 = 8 cm²

A) Determine the magnetic flux ΦB

where ; ΦB  = BA

ΦB = ( 5 * 10⁻³ ) * ( 4 * 10⁻² ) * ( 2 * 10⁻² ) Tm²

      =  4 * 6⁻⁶ Tm²

B) Determine estimated emf induced

To determine the estimated emf we will apply Faraday's law

Ε = Bℓυ ---- ( 2 )

where : B = 5 * 10⁻³ T,  ℓ = 2 * 10⁻² m,  υ = 2 * 10⁻² m/s

insert values into equation 2

E = ( 5 * 10⁻³ ) * ( 2 * 10⁻² ) * ( 2 * 10⁻² )

  = 2 * 10⁻⁶ v

Hence we can conclude that The magnetic flux ΦB is 4 * 6⁻⁶ Tm² and The estimated emf induced is  2 * 10⁻⁶ v

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