Question

A at
oil of wire has an area A, N turns, and a resistan
e R. It is situated in a magneti
eld,
su
h that the normal to the
oil is parallel to the magneti
eld. The
oil is then rotated through
an angle of φ = 90◦
, so that the normal be
omes perpendi
ular to the magneti
eld. The
oil has
an area of 1.5 × 10−3 m2
, 50 turns, and a resistan
e of 140 Ω. During the time while it is rotating, a

harge of 8.5 × 10−5 C ows in the
oil. Cal
ulate the magnitude of the magneti
eld?

Answer 1

Question:

A flat coil of wire has an area A, N turns, and a resistance R. It is situated in a magnetic field, such that the normal to the coil is parallel to the magnetic field. The coil is then rotated through an angle of 90°, so that the normal becomes perpendicular to the magnetic field. The coil has an area of 1.5×10⁻³ m² , 50 turns, and a resistance of 140 Ω. During the time while it is rotating, a charge of 8.5×10⁻⁵ C flows in the coil. Calculate the magnitude of the magnetic field.

Solution:

The electromotive force is

$$E=N\frac{dAB}{dt}.$$

The EMF, on the other hand, is

$$E=RI=R\frac{qd}{dt},\\ \space\\ R\frac{qd}{dt}=NA\frac{dB}{dt}, \\ Rdq=NAdB,$$

and we know that when the field changed from zero to B, the charge changed from 0 to Q:

$$RQ=NBA,\\ B=\frac{RQ}{NA}=\frac{140\cdot8.5\cdot10^{-5}}{50\cdot1.5\cdot10^{-3}}=0.159\text{ T}.$$