A 30.0 cm x 60.0 cm rectangular circuit containing a 15.0 ohm resistor is perpen

Question

A 30.0 cm x 60.0 cm rectangular circuit containing a 15.0 ohm resistor is perpendicular to a uniform magnetic field that starts out at 2.40 T and steadily decreases at 0.340 T/s. (See the figure1.)

While this field is changing, what does the ammeter read?

A 30.0 cm x 60.0 cm rectangular circuit containing a 15.0 ohm resistor is perpendicular to a uniform magnetic field that starts out at 2.40 T and steadily decreases at 0.340 T/s. (See the figure1.) While this field is changing, what does the ammeter read?

Explanation / Answer

V = IR
I = V/R

For our purposes, V = , so I = /R

= - / t
= BAcos
= angle between magnetic field and vector normal to the area

In this case, = 0, as both the normal vector and the magnetic field are perpendicular to the loop.

I = - / (Rt)
= -(BAcos) / (Rt)
= -(B)(Acos) / (Rt)
= -(B / t)(Acos / R)
= -(-0.340 T/s)(30.0 * 10^-2 m)(60.0 * 10^-2 m)(cos 0) / (15.0 )
-->[B / t < 0 as the magnetic field is decreasing]
= 0.00408 A

Rounding to three sig figs, the ammeter reads 4.08 * 10^-3 A.

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