Chapter 11, Problem 1P

For the electromagnet in Fig. 11.75:

a. Find the flux density in Wb/m².

b. What is the flux density in teslas?

c. What is the applied magnetmotive force?

d. What would the reading of the meter in Fig. 11.14 read in gauss?

Fig. 11.75

To determine

(a)

The value of flux density.

Answer to Problem 1P

The value of flux density is $0.04\frac{\text{Wb}}{{\text{m}}^2}$.

Explanation of Solution

Concept used:

Write the expression for magnetic flux density:

  $B=\frac{\varphi }{A}$   ............(1)

Here, $B$ is magnetic flux density, $\varphi$ is the flux and $A$ is the area.

Calculation:

Substitute $4\times {10}^{-4}\text{Wb}$ for $\varphi$ and $0.01{\text{m}}^2$ for $A$ in equation (1).

  $\begin{array}{c}B=\frac{4\times {10}^{-4}\text{Wb}}{0.01{\text{m}}^2}\\ =0.04\frac{\text{Wb}}{{\text{m}}^2}\end{array}$

Conclusion:

Thus,value of flux density is $0.04\frac{\text{Wb}}{{\text{m}}^2}$.

To determine

(b)

The flux density in tesla.

Answer to Problem 1P

The value of flux density in tesla is $0.04\text{T}$.

Explanation of Solution

Concept used:

  $1\text{T}=\text{1}\frac{\text{Wb}}{{\text{m}}^{\text{2}}}$

Calculation:

The value of flux density $B$ is $0.04\frac{\text{Wb}}{{\text{m}}^2}$.

  $\begin{array}{c}B=0.04\frac{\text{Wb}}{{\text{m}}^2}\left(\frac{1\text{T}}{1\frac{\text{Wb}}{{\text{m}}^2}}\right)\\ =0.04\text{T}\end{array}$

Conclusion:

Thus, value of flux density in tesla is $0.04\text{T}$.

To determine

(c)

The value of applied magnetomotive force.

Answer to Problem 1P

The value of applied magnetomotive force is $88\text{At}$.

Explanation of Solution

Concept used:

Write the expression for magnetomotive force.

  $F=NI$   ............(2)

Here, $F$ is magnetomotive force, $N$ is number of turns and $I$ is value of current.

Calculation:

Substitute $40$ for $N$ and $2.2\text{A}$ for $I$ in equation (2).

  $\begin{array}{c}F=40\left(2.2\text{A}\right)\\ =88\text{At}\end{array}$

Conclusion:

Thus,value of applied magnetomotive force is $88\text{At}$.

To determine

(d)

The value of flux density in gauss.

Answer to Problem 1P

The value of flux density in gauss is $400\text{gauss}$.

Explanation of Solution

Concept used:

  $1\text{T}={\text{10}}^4\text{gauss}$

Calculation:

The value of flux density $B$ in tesla is $0.04\text{T}$.

  $\begin{array}{c}B=0.04\text{T}\left(\frac{1\text{gauss}}{{10}^{-4}\text{T}}\right)\\ =400\text{gauss}\end{array}$

Conclusion:

Thus, the value of flux density in gauss is $400\text{gauss}$.