The magnetic field in a loudspeaker is 0.2 T.
The wire consists of 308 turns wound on a
4.12 cm diameter cylindrical form. The resistance of the wire is 8.2 Ω.
Find the force exerted on the wire when
15.8 V is placed across the wire.
Answer in units of N
To find the force exerted on the wire, we can use the equation:
F = B * I * L
Where:
F is the force exerted on the wire,
B is the magnetic field strength,
I is the current flowing through the wire, and
L is the length of the wire.
To find the current (I) flowing through the wire, we can use Ohm's Law:
I = V / R
Where:
I is the current,
V is the voltage, and
R is the resistance.
Given that the voltage (V) across the wire is 15.8 V and the resistance (R) is 8.2 Ω, we can calculate the current (I) as follows:
I = 15.8 V / 8.2 Ω
Now, we need to find the length (L) of the wire. The wire is wound on a cylindrical form, and we are given the number of turns (308) and the diameter of the form (4.12 cm).
The length of the wire (L) can be calculated using the formula for the circumference of a circle:
C = 2πr
Where:
C is the circumference, and
r is the radius of the cylindrical form.
The radius (r) can be calculated by dividing the diameter (d) by 2:
r = d / 2
Now, we can calculate the length (L) of the wire using the circumference formula:
L = C * N
Where:
L is the length of the wire,
C is the circumference, and
N is the number of turns.
Given that the diameter (d) is 4.12 cm, the radius (r) is 2.06 cm, and the number of turns (N) is 308, the length (L) of the wire can be calculated as follows:
r = 2.06 cm
C = 2π * 2.06 cm
L = C * 308 turns
Finally, substituting the values we have obtained into the formula for the force (F), we can calculate the force exerted on the wire:
F = B * I * L
Given that the magnetic field strength (B) is 0.2 T, the current (I) is calculated in the previous step, and the length (L) is calculated in the previous step, we can calculate the force (F) exerted on the wire.
Please substitute the given values into the formulas to get the final answer.