The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and the cone. (b) The voice coil and cone have a combined mass of 0.0200 kg. Find their acceleration Magnetic field Cone Permanent magnet WORK ON

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### Magnetic Force on a Speaker's Voice Coil

The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A.

(a) **Determine the magnetic force that acts on the coil and the cone.**
(b) **The voice coil and cone have a combined mass of 0.0200 kg. Find their acceleration.**

#### Diagram Explanation

The provided diagram consists of three main parts:

1. **Left Section:**
   - This shows a permanent magnet with labeled components.
   - A voice coil is depicted adjacent to a speaker cone.
   - Black panel of receiver connected via a wire to the speaker terminals.

2. **Right Section:**
   - Demonstrates the magnetic field and the voice coil in greater detail.
   - A uniform magnetic field region labeled "Magnetic field" is shown.
   - The voice coil in the magnetic field is illustrated with force vectors denoted by \( \mathbf{F} \).

#### Solutions Breakdown:
1. **Determine the Magnetic Force:**

Use the formula for the magnetic force on a current-carrying conductor in a magnetic field:
\[ F = n \cdot L \cdot I \cdot B \]

where:
- \( n \) = number of turns (55)
- \( L \) = length of one turn (circumference of the coil) \( = \pi \times \text{diameter} \)
- \( I \) = current (2.0 A)
- \( B \) = magnetic field (0.10 T)

Length of one turn \( L \):
\[ L = \pi \times 0.0025 \, \text{m} \approx 0.00785 \, \text{m} \]

Now, calculating the total force \( F \):
\[ F = 55 \times 0.00785 \, \text{m} \times 2.0 \, \text{A} \times 0.10 \, \text{T} 
= 55 \times 0.00157 \, \text{N} 
= 0.08635 \, \text{N} \]

2. **Find the Acceleration:**

Use Newton's second law:
\[ F = m \cd
Transcribed Image Text:### Magnetic Force on a Speaker's Voice Coil The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) **Determine the magnetic force that acts on the coil and the cone.** (b) **The voice coil and cone have a combined mass of 0.0200 kg. Find their acceleration.** #### Diagram Explanation The provided diagram consists of three main parts: 1. **Left Section:** - This shows a permanent magnet with labeled components. - A voice coil is depicted adjacent to a speaker cone. - Black panel of receiver connected via a wire to the speaker terminals. 2. **Right Section:** - Demonstrates the magnetic field and the voice coil in greater detail. - A uniform magnetic field region labeled "Magnetic field" is shown. - The voice coil in the magnetic field is illustrated with force vectors denoted by \( \mathbf{F} \). #### Solutions Breakdown: 1. **Determine the Magnetic Force:** Use the formula for the magnetic force on a current-carrying conductor in a magnetic field: \[ F = n \cdot L \cdot I \cdot B \] where: - \( n \) = number of turns (55) - \( L \) = length of one turn (circumference of the coil) \( = \pi \times \text{diameter} \) - \( I \) = current (2.0 A) - \( B \) = magnetic field (0.10 T) Length of one turn \( L \): \[ L = \pi \times 0.0025 \, \text{m} \approx 0.00785 \, \text{m} \] Now, calculating the total force \( F \): \[ F = 55 \times 0.00785 \, \text{m} \times 2.0 \, \text{A} \times 0.10 \, \text{T} = 55 \times 0.00157 \, \text{N} = 0.08635 \, \text{N} \] 2. **Find the Acceleration:** Use Newton's second law: \[ F = m \cd
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