Question

A 40-turn, 4.0-cm-diameter coil with *R*=0.40Ω surrounds
a 3.0-cm-diameter solenoid. The solenoid is 20 cm long and has 200
turns. The 60 Hz current through the solenoid is
*I*=*I*0sin(2*π**f**t*).

What is *I*0 if the maximum induced current in the coil
is 0.20 A?

Answer #1

**DATA:**

**SOLUTION**

**The current through the
coil is defined as:**

**Where
is defined as:**

**Where, is the magnetic
flux through the solenoid, and can be written as
follows:**

**But, because
is in
the direction of , so:**

**Being, the area of the
solenoid, so:**

**Now, the magnetic field
is given
by:**

**But, is given
by:**

**Therefore, replacing (6)
into equation (5) we have:**

**Replacing (7) and (4) into
equation (3):**

**Replacing (8) into equation
(2) we have:**

**or**

**taking
derivative:**

**or**

**Replacing (12) into equation
(1) we have:**

**Now, the current through the
coil is maximum when:**

**Therefore, equation (13) can
be written as:**

**Isolating we
obtain:**

**Finally, replacing values of
DATA given into equation (15) we have:**

**Solving we
obtain:**

A 40-turn, 4.0-cm-diameter coil with R=0.40Ω surrounds
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turns. The 60 Hz current through the solenoid is
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