Question

Marvin uses a long copper wire with resistivity 1.68 x 10^-8 Ω⋅m and diameter 1.00 x 10^−3​​ m to create a solenoid that has a 3.00 cm radius.

Part A: Calculate the total resistance if Marvin uses 11.3 meters of wire to create the solenoid.

Part B: Calculate how many turns are in the solenoid.

Part C: A 3.00 Volt potential difference is applied across the wires of the solenoid. Calculate the current that passes through the solenoid.

Part D: If the coils in the solenoid are separated so that they are evenly spaced across a total length of 0.1 m, what is the magnitude of the magnetic field along the central axis inside of the solenoid?

Answer 1

Step-by-step explanation:

resistivity of copper, ρ = 1.68 x 10^-8 ohm - m

diameter = 1 x 10^-3 m

radius of wire, r = 0.5 x 10^-3 m

Radius of solenoid, r' = 3 cm

(A)

Length of wire, l = 11.3 m

Let the resistance of wire is R.

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

where, A is the crossection of wire

A = 3.14 x 0.5 x 10^-3 x 0.5 x 10^-3 = 7.85 x 10^-7 m²

`R= (1.68* 10^(-8)* 11.3)/(7.85* 10^(-7))`

R = 0.24 ohm

(B)

Let the number of turns is N.

Length of wire = N x circumference of one turn

11.3 = N x 2 x 3.14 x 0.03

N = 60

(C)

V = 3 V

R = 0.24 ohm

V = i x R

3 = i x 0.24

i = 12.5 A

(D) number of turns per unit length, n = N / 0.1 = 60 / 0.1 = 600

The magnetic field is given by

`B = \mu _(0)ni`

`B = 4 * 3.14 * 10^(-7)* 600* 12.5`

B = 9.42 x 10^-3 Tesla

Answer 2

Answer with Explanation:

We are given that

Resistivity of copper wire=
`\rh0=1.68* 10^(-8)\Omega m`

Diameter=d=
`1.00* 10^(-3) m`

Radius of copper wire=
`r=(d)/(2)=(1)/(2)* 10^(-3) m`

Radius of solenoid=r'
`=3 cm=3* 10^(-2) m`

1 m=100 cm

a.Length of wire=l=11.3 m

Area of wire=A=
`\pi r^2`

Where
`\pi=3.14`

A=
`3.14* ((1)/(2)* 10^(-3))^2`

Resistance, R=
`\rho (l)/(A)`

Using the formula

`R=1.68* 10^(-8)*(11.3)/(3.14* ((1)/(2)* 10^(-3))^2)`

`R=0.24\Omega`

B.Length of solenoid=
`2\pi r'=2* 3.14* 3* 10^(-2)=0.188` m

Number of turns=
`n_0=(l)/(2\pi r')=(11.3)/(0.188)`

`n_0`=60

C.Potential difference,V=3 V

Current,I=
`(V)/(R)`

I=
`(3)/(0.24)=12.5 A`

D.Total length =0.1 m

Number of turns per unit length,n=
`(60)/(0.1)=600`

Magnetic field along central axis inside of the solenoid,B=
`\mu_0 nI`

`B=4\pi* 10^(-7)* 12.5* 600=9.42* 10^(-3) T`