A metal strip 6.50 cm long. 0.850 cm wide, and 0.760 mm thick moves with constant velocity v⃗

step 1 So in this question we have a metal strip that is 6 .5 meter long this metal strip is 6 .5 meter

A metal strip 6.50 cm long. 0.850 cm wide, and 0.760 mm...

A metal strip $6.50 \mathrm{~cm}$ long. $0.850 \mathrm{~cm}$ wide, and $0.760 \mathrm{~mm}$ thick moves with constant velocity $\vec{v}$ through a uniform magnetic field $B=$ $1.20 \mathrm{mT}$ directed perpendicular to the $\mathbf{X}$ strip, as shown in Fig. $28-34$. A potential difference of $3.90 \mu \mathrm{V}$ is measured $\mathrm{x}$ between points $x$ and $y$ across the strip. Calculate the speed $v$.

A metal strip $6.50 \mathrm{~cm}$ long. $0.850 \mathrm{~cm}$ wide, and $0.760 \mathrm{~mm}$ thick moves with constant velocity $\vec{v}$ through a uniform magnetic field $B=$ $1.20 \mathrm{mT}$ directed perpendicular to the $\mathbf{X}$
strip, as shown in Fig. $28-34$. A potential difference of $3.90 \mu \mathrm{V}$ is measured $\mathrm{x}$ between points $x$ and $y$ across the strip. Calculate the speed $v$.

Key Concepts

Motional EMF

This concept describes the electromotive force induced in a conductor due to its motion through a magnetic field. When a conductor moves with velocity through a magnetic field, the free charges within experience a force due to the magnetic field, which results in a separation of charge and therefore an induced potential difference across the conductor. The induced EMF is often calculated using the relation ? = B ? L ? v, where B is the magnetic field strength, L is the effective length of the conductor, and v is the velocity of the conductor.

Lorentz Force

The Lorentz force is the force experienced by moving charge carriers in a magnetic field, given by F = q(v × B), where q is the electric charge. This force is responsible for the separation of charges in a moving conductor, leading to the creation of an electric field and resultant potential difference, which is the basis for the motional EMF.

Electromagnetic Induction

This is the overarching principle that a change in magnetic flux through a circuit induces an electromotive force. In the context of a moving conductor in a steady magnetic field, the continuous movement of the conductor changes the magnetic flux experienced by it, thereby inducing an EMF. This principle underpins many practical applications such as electric generators.

Unit Conversions and Dimensional Analysis

Accurate problem solving in electromagnetism requires careful conversion between units (e.g., converting centimeters to meters or millimeters to meters) to ensure that all quantities are expressed in consistent units. Dimensional analysis helps in verifying that derived equations and calculations follow the correct physical dimensions, leading to valid numerical results.

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