In Fig. 28-57, the two ends of a U-shaped wire of mass m= 10.0 g and length L=20.0 cm are imme

step 1 For this problem on the topic of magnetic fields, we are shown two ends of a U -shaped wire, whi

In Fig. 28-57, the two ends of a U-shaped wire of mass m=...

In Fig. $28-57$, the two ends of a U-shaped wire of mass $m=$ $10.0 \mathrm{~g}$ and length $L=20.0 \mathrm{~cm}$ are immersed in mercury (which is a conductor). The wire is in a uniform field of magnitude $B=0.100 \mathrm{~T}$. A switch (unshown) is rapidly closed and then reopened, sending a pulse of current through the wire, which causes the wire to jump upward. If jump height $h=3.00 \mathrm{~m}$, how much charge was in the pulse? Assume that the duration of the pulse is much less than the time of flight. Consider the definition of impulse (Eq. $9-30)$ and its relationship with momentum (Eq. 9-31). Also consider the relationship between charge and current (Eq. 26-2).

In Fig. $28-57$, the two ends of a U-shaped wire of mass $m=$ $10.0 \mathrm{~g}$ and length $L=20.0 \mathrm{~cm}$ are immersed in mercury (which is a conductor). The wire is in a uniform field of magnitude $B=0.100 \mathrm{~T}$. A switch (unshown) is rapidly closed and then reopened, sending a pulse of current through the wire, which causes the wire to jump upward. If jump height $h=3.00 \mathrm{~m}$, how much charge was in the pulse? Assume that the duration of the pulse is much less than the time of flight. Consider the definition of impulse (Eq. $9-30)$ and its
relationship with momentum (Eq. 9-31). Also consider the relationship between charge and current (Eq. 26-2).

Key Concepts

Conservation of Energy and Kinematics

When an object is propelled upward, its initial kinetic energy is converted into gravitational potential energy at the peak of its height. The relationship mgh = ½ m v² (or equivalently using kinematics, v = ?(2gh)) allows one to connect the impulse-induced momentum (or velocity) of the object to the height it reaches, linking energy concepts with momentum and impulse.

Charge-Current Relationship

Current represents the rate at which charge flows, and the relationship between charge and current is given by the equation Q = I ?t, where Q is the total charge passing through a point over a time interval ?t. This connection is vital when determining the amount of charge involved in a short current pulse.

Impulse

Impulse is defined as the integral of force with respect to time and represents the change in momentum of an object. In problems where a short-duration force (pulse) is applied, the impulse can be equated to the momentum gained by the object. This concept is critical when relating the sudden force applied to an object with its acquired velocity and subsequent motion.

Lorentz Force on a Current-Carrying Conductor

A conductor carrying current in a magnetic field experiences a force given by the product of its current, the length of the conductor, and the magnetic field strength (F = I L B) when the conductor is oriented perpendicularly to the field. This concept shows how a current pulse can impart a mechanical force to the conductor, leading to motion.

Transcript

Please give Ace some feedback