91影视

We have given that, the solenoid has 40 cm diameter and 1.0 m length. A 100 A current creates a 5.0 T magnetic field inside the solenoid.

To calculate the total energy of solenoid, we have to determine volume and energy density.

The formula to calculate volume is :

$V_{sol}=蟺{r^2}_{sol}l$

Here, $V_{sol}$= volume of solenoid

$r_{sol}$= radius of solenoid

$l$= length of solenoid

Substituting the values in the formula :

localid="1651030697382" $V=蟺脳{(0.20m)}^2脳(1.0m)$

$V=0.126m^3$

Now we will calculate the the value of energy density of solenoid.

The formula of energy density is :

${渭}_B=\frac{1}{2{渭}_0}{B}^2$

Here, ${渭}_B$= Energy density

${渭}_{0=}$Permeability constant

$B$= Magnetic field

Substituting the values in the formula :

localid="1651030882723" ${渭}_B=\frac{{(5.0T)}^2}{2(4蟺脳{10}^{-7}H/m)}$

localid="1651031066068" ${渭}_B=9.95脳{10}^{6}J/m^3$

Now we will calculate the value of stored energy.

The formula for the stored energy is :

$U_{tot}={渭}_B{V}_{sol}$

localid="1651031003274" $U_{tot}=(9.95脳{10}^{6}J/m^{-3})(0.120m^3)$

$U_{tot}=1.25脳{10}^{6}J$

The stored energy of solenoid is$1.25脳{10}^{6}J$.

We have given that, the solenoid has 40 cm diameter and 1.0 m length. A 100 A current creates a 5.0 T magnetic field inside the solenoid.

The formula for the number of turns of wire is :

$N=\frac{B{l}_{sol}}{{渭}_{0}I}$

Here, $N$= Number of turns of wire

$l_{sol}$= Length of solenoid

${渭}_0$= Permeability constant

$I$= Current

Substituting the values in the formula :

$N=\frac{(1.0m)(5.0T)}{(4蟺脳{10}^{-7}H/m)(100A)}$

$N=4.0脳{10}^4$

Total number of turns is$4.0脳{10}^4$.