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Question

A wire is placed along a parabola y=4x2 from x =-1 to x = +1 with a current of 10 A flowing through it and a uniform cross-sectional area of 0.1m2. What is the direction and magnitude of the current density vector of this wire?

A
100A/m2 in the positive x direction
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B
100A/m2 in the negative x direction
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C
1A/m2 in the positive y direction
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D
100A/m2 at every cross-section with its direction tangential to the wire in the direction of current.
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Solution

The correct option is D 100A/m2 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 |J|=IA where I is the current and A is the cross-sectional area. Here J=100.1=100Am2

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