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Electricity and Magnetism

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Moderate

Current Due to an Electric Field

EANDM-HRMIHY

Figure 1 depicts a wire aligned along the $\hat{z}$-axis, whose cross-section has a radius of $r = 2.68 \text{ mm}$.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

The conductance of the wire is equal to:

$$\sigma = 3.20 \times 10^4 \; \rm{\frac{siemens}{m}}$$

An electric field exists in this region, which is given by:

$$\vec{E} = a\hat{x} + b\hat{y} + c\hat{z}$$

…where:

  • $a = 3.50 \; \rm{\cfrac{N}{C}}$
  • $b = 4.60 \; \rm{\cfrac{N}{C}}$
  • $c = 7.90 \; \rm{\cfrac{N}{C}}$

What is the current passing through this wire due to the electric field?

A

$I = 6.90 \text{ nA}$

B

$I = 5.70 \text{ A}$

C

$I = 5.57 \text{ nA}$

D

$I = 7.07 \text{ A}$