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(a) At room temperature, what is the strength of the electric field in a

12-gauge copper wire (diameter 2.05mm) that is needed to cause a 4.50-A

current to flow? (b) What field would be needed if the wire were made of silver

instead?

Short Answer

Expert verified

(a)The strength of the electric field in a 12-gauge copper wire that is needed to

cause a 4.50-Acurrent to flow is 23.45×10-3VM.

(b)The electric field that needed if wire were made of silver instead is 20.045×10-3Vm.

Step by step solution

01

Define the electric field.

The electric force per unit charge is known as electric.

E=ρIA

Here, Iis current in ampere A, ρis resistivity in ohms meter Ω.mand is the

area in m2.

02

Determine the strength of the electric field in copper wire.

(a)

Consider the given resistivity, current and the diameter of the wire.

ρ=1.72×10-8Ω.mI-4.50Ad=2.05×10-3m

Solve for the electric field strength.

E=ρIA

Substitute the values and solve.

E=1.72×10-84.50π42.05×10-8=23.45×10-3V/m

Hence, strength of the electric field in a 12-gauge copper wire that is needed to

cause a 4.50-Acurrent to flow is 23.45×10-3Vm.

03

Determine the strength of the electric field in silver wire.

(b)

Given the value of the resistivity is ρ=1.47×10-8Ω.m.

The strength of the electric field is:

E=ρIA

Substitute the value and solve.

E=1.47×10-84.50π42.05×10-8=20.045×10-3V/m

Hence, electric field that needed if wire were made of silver instead is 20.045×10-3Vm.

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