The magnetic field in a loudspeaker is 0.18 T. The wire consists of 150 turns wound on a 1.4 cm diameter cylindrical form. The resistance of the wire is 8.0 . Find the force exerted on the wire when 15 V is placed across the wire.
To find the force exerted on the wire, we can use the equation for the force on a current-carrying wire in a magnetic field:
F = BIL
where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.
First, let's find the current passing through the wire. We can use Ohm's Law:
V = IR
where V is the voltage, I is the current, and R is the resistance.
Rearranging the equation, we have:
I = V / R
Substituting the given values, we have:
I = 15 V / 8.0 Ω
I ≈ 1.875 A
Next, let's calculate the length of the wire wound on the cylindrical form. The wire is wound into 150 turns, and the diameter of the form is given as 1.4 cm. The length of the wire would be the circumference of the cylindrical form multiplied by the number of turns:
C = πd
where C is the circumference and d is the diameter.
C = π(1.4 cm)
C ≈ 4.4 cm
Now, we convert the length from centimeters to meters:
L = 0.044 m
Finally, we can calculate the force using the formula:
F = BIL
Substituting the given values:
F = (0.18 T)(1.875 A)(0.044 m)
F ≈ 0.15 N
Therefore, the force exerted on the wire when 15 V is placed across it is approximately 0.15 N.