Question

A closely wound rectangular coil of 100 turns has dimensions of 27.0 cm by 50.0 cm . The plane of the coil is rotated from a position where it makes an angle of 37.0 ∘ with a magnetic field of 1.20 T to a position perpendicular to the field. The rotation takes 9.00×10−2 s . (Note that the coil is perpendicular to the area vector of the coil.) What is the average EMF induced in the coil?

Answer 1

`\epsilon =71.677V` induced.

Step-by-step explanation:

We define all our variables,

`B=1.2T`

`A=0.27m*0.50m`

`\theta= 90-37`

`\Delta T= 0.09s`

`N= 100`

EMF induced is given through the expression

`\epsilon = (-N\Delta \Phi)/(\Delta t)`

Here we understand
`\Phi` as

`\Phi = BAcos\theta`

We proceed to calculate the entire Initial Flow as the final, as well

`\Phi_i=(1.2)(0.27*0.5)cos(90-37) = 0.09749Tm^2`

Final Flow

`\Phi_f=(1.2)(0.27*0.5)= 0.162Tm^2`

Now, if
`\Delta t = 0.09s`,

`\epsilon= (100)(0.162Tm^2 - 0.09749Tm^2)/(0.09s)`

`\epsilon =71.677V` induced.

NOTES:

• It is necessary to make two small notes regarding the development of the exercise. The subtraction of the angles is used since the exercise indicates that the angle is between the field B and the Plane. However, the measurement between the Area and the field is required b.
• Negative signs can be neglected because it is understood that this is a reference to know which direction has the highest potential.