## An aluminum “12 gauge” wire has a diameter d of 0.205 centimeters. The resistivity ρ of aluminum is 2.75×10−8 ohm-meters. The electric field

Question

An aluminum “12 gauge” wire has a diameter d of 0.205 centimeters. The resistivity ρ of aluminum is 2.75×10−8 ohm-meters. The electric field in the wire changes with time as E(t)=0.0004t2−0.0001t+0.0004 newtons per coulomb, where time is measured in seconds.

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5 months 2021-09-01T10:51:03+00:00 1 Answers 0 views 0

1. Complete Question

An aluminum “12 gauge” wire has a diameter d of 0.205 centimeters. The resistivity ρ of aluminum is 2.75×10−8 ohm-meters. The electric field in the wire changes with time as E(t)=0.0004t2−0.0001t+0.0004 newtons per coulomb, where time is measured in seconds.

I = 1.2 A at time 5 secs.

Find the charge Q passing through a cross-section of the conductor between time 0 seconds and time 5 seconds.

The charge is

Explanation:

From the question we are told that

The diameter of the wire is

The radius of  the wire is

The resistivity of aluminum is

The electric field change is mathematically defied as

Generally the charge is  mathematically represented as

Where A is the area which is mathematically represented as

So

Therefore

substituting values

From the question we are told that t =  5 sec