Question
A wire with cross-sectional area $A$ carries a current I. Assuming the wire is ohmic, show that the electric field strength $E$ in the wire is proportional to the current per unit area (I/A) and identify the constant of proportionality.
Step 1
Step 1: We know that the resistance $R$ of a conductor of length $L$ and cross-sectional area $A$ is given by the formula: \[R = \rho \frac{L}{A}\] where $\rho$ is the resistivity of the conductor. Show more…
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A wire with cross-sectional area $A$ carries a current $I$ Show that the electric field strength $E$ in the wire is proportional to the current per unit area $(I / A)$ and identify the constant of proportionality. [Hint: Assume a length $L$ of wire. How is the potential difference across the wire related to the electric field in the wire? (Which is uniform?) Use $V=I R$ and the connection between resistance and resistivity.]
A wire of radius $R$ carries a current $i$. The current density is given by $J=J_{0}(1-r / R),$ where $r$ is measured from the center of the wire and $J_{0}$ is a constant. Use Ampere's Law to find the magnetic field inside the wire at a distance $r<R$ from the central axis.
A wire of radius $R$ carries current $i$. The current density is given by $J=J_{0}(1-r / R),$ where $r$ is measured from the center of the wire and $J_{0}$ is a constant. Use Ampere's Law to find the magnetic field inside the wire at a distance $r<R$ from the central axis.
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