In the figure, a metal wire of mass m = 28.9 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 2.62 cm. The track lies in a vertical uniform magnetic field of magnitude 51.2 mT. At time t=0 s, device G is connected to the rails, producing a constant current i = 7.16 mA in the wire and rails (even as the wire moves). At t = 64.0 ms, what are the wire's (a) speed and (b) direction of motion? (a) Number (b) m 727 Units
In the figure, a metal wire of mass m = 28.9 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 2.62 cm. The track lies in a vertical uniform magnetic field of magnitude 51.2 mT. At time t=0 s, device G is connected to the rails, producing a constant current i = 7.16 mA in the wire and rails (even as the wire moves). At t = 64.0 ms, what are the wire's (a) speed and (b) direction of motion? (a) Number (b) m 727 Units
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Transcribed Image Text:### Question:
**Problem Statement:**
In the figure, a metal wire of mass \( m = 28.9 \, \text{mg} \) can slide with negligible friction on two horizontal parallel rails separated by distance \( d = 2.62 \, \text{cm} \). The track lies in a vertical uniform magnetic field of magnitude \( 51.2 \, \text{mT} \). At time \( t = 0 \, \text{s} \), device \( G \) is connected to the rails, producing a constant current \( i = 7.16 \, \text{mA} \) in the wire and rails (even as the wire moves). At \( t = 64.0 \, \text{ms} \), what are the wire's (a) speed and (b) direction of motion?
**Graph Description:**
- A diagram depicting a metal wire \( m \), lying between two parallel rails separated by a distance \( d \).
- The rails are positioned in such a way that the wire \( m \) can move horizontally on them.
- A magnetic field \( \mathbf{B} \) is indicated perpendicular to the plane of the rails and directed vertically.
- The current \( i \) flows along the wire \( m \) and the rails.
- Device \( G \) is shown connected to the rails, sustaining the current \( i \).
- The direction of the magnetic force \( \mathbf{F} \) acting on the wire is shown in accordance with the right-hand rule.
**Questions:**
(a) Speed of the wire:
- Number: \( \_\_\_\_\_\_\_\_\_\_\_\_\_ \)
- Units: \( \_\_\_\_\_\_\_\_\_\_\_\_\_ \)
(b) Direction of motion:
(Selection Box)
### Educational Insight:
This problem involves the application of the Lorentz force law in the context of a magnetic field affecting a current-carrying conductor. Students are expected to:
1. Understand and apply the formula for the magnetic force acting on a current-carrying wire.
2. Recognize how the magnetic field, current, and resulting force interact according to the right-hand rule.
3. Calculate the resultant acceleration and speed of the wire using fundamental principles of dynamics and electromagnetism.
Be sure to consider the components and units carefully in order to arrive at an accurate
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