Question

A wire is placed along a parabola $y=4x^2$ from x =-1 to x = +1 with a current of 10 A flowing through it and a uniform cross-sectional area of $0.1m^2$. What is the direction and magnitude of the current density vector of this wire?

• A. $100A/m^2$ in the positive x direction
• B. $100A/m^2$ in the negative x direction
• C. $1A/m^2$ in the positive y direction
• D. $100A/m^2$ at every cross-section with its direction tangential to the wire in the direction of current.

Answer 1

The correct option is D $100A/m^2$ at every cross-section with its direction tangential to the wire in the direction of current.

Current density vector is defined for cross-sections and for every different cross-section there is a different current density vector!
The magnitude however in this case will remain the same. That’s because $|\overrightarrow{J}|=\frac{I}{A}$ where I is the current and A is the cross-sectional area. Here $J=\frac{10}{0.1}=100\frac{A}{m^2}$