Question

current density in the wire if an electric field E is passing through it. Write this in terms of the resistivity and the other variables in the problem.

Answer 1

Complete Question

The complete question is shown on the first and second uploaded image

Note : The resistance is R = 147 Ohms

Answer:

The current density in terms of resistivity is
`J = (E)/(\rho)`

The current is
`I = 176 *10^(-3) \ A`

Step-by-step explanation:

From the question we are told that

The length of the wire is
`L = 2.75 \ m`

The radius of the circular cross-sectional area is
`r = 1.76 \ mm = 0.00176 m`

The electric field strength is E =9.41 V/m

Generally the current density is mathematically represented as

`J = (E)/(\rho)`

Here
`\rho` is the resistivity of the wire which is mathematically represented as

`\rho = (R * A)/(L)`

So

`J = (EL )/(RA)`

Here A is the cross-sectional area which is mathematically represented as

`A =\pi r^2`

So

`J = (EL )/(R * \pi r^2 )`

Generally the current density can also be mathematically represented as

`J = (I)/(A)`

So

`(EL )/(RA) = (I)/(A)`

=>
`I = (EL)/(R)`

=>
`I = (9.41 2.75)/(147 )`

=>
`I = 176 *10^(-3) \ A`