Chapter 19, Problem 76QAP

To determine

(a)

Current in the dryer

Answer to Problem 76QAP

Current in the dryer= $15.1\text{ A}$

Explanation of Solution

Given info:

  $\begin{array}{l}\text{Voltage = }110\text{ V}\\ \text{Power = }1650\text{ W}\\ \text{Distance of the current from user head = }3\text{ cm}\\ {\text{Earth's magnetic field = 5*10}}^{\text{-5}}\text{ T}\end{array}$

Formula used:

  $\begin{array}{l}P=\frac{V^2}{R}\\ V=\text{potential}\\ P=\text{Power}\\ R=\text{resistance}\end{array}$

  $\begin{array}{l}B=\frac{{\mu }_{0}I}{2\pi d}\\ B=\text{Magnetic field}\\ {\mu }_0=\text{permeability of free space}\\ I=\text{Current in wire}\\ d=\text{Radius from the wire}\end{array}$

  $\begin{array}{l}V=IR\\ V=\text{potential}\\ I=\text{Current in wire}\\ R=\text{resistance}\end{array}$

Calculation:

  $\begin{array}{l}P=\frac{V^2}{R}\\ 1650=\frac{{110}^2}{R}\\ R=7.3\Omega \end{array}$

  $\begin{array}{l}V=IR\\ 110=I*7.3\\ I=15.1\text{ A}\end{array}$

Conclusion:

Current in the dryer= $15.1\text{ A}$

To determine

(b)

Resistance in the dryer

Answer to Problem 76QAP

Resistance in the dryer= $7.3\Omega$

Explanation of Solution

Given info:

  $\begin{array}{l}\text{Voltage = }110\text{ V}\\ \text{Power = }1650\text{ W}\\ \text{Distance of the current from user head = }3\text{ cm}\\ {\text{Earth's magnetic field = 5*10}}^{\text{-5}}\text{ T}\end{array}$

Formula used:

  $\begin{array}{l}P=\frac{V^2}{R}\\ V=\text{potential}\\ P=\text{Power}\\ R=\text{resistance}\end{array}$

  $\begin{array}{l}B=\frac{{\mu }_{0}I}{2\pi d}\\ B=\text{Magnetic field}\\ {\mu }_0=\text{permeability of free space}\\ I=\text{Current in wire}\\ d=\text{Radius from the wire}\end{array}$

  $\begin{array}{l}V=IR\\ V=\text{potential}\\ I=\text{Current in wire}\\ R=\text{resistance}\end{array}$

Calculation:

  $\begin{array}{l}P=\frac{V^2}{R}\\ 1650=\frac{{110}^2}{R}\\ R=7.3\Omega \end{array}$

Conclusion:

Resistance in the dryer= $7.3\Omega$

To determine

(c)

Magnetic field does the dryer produce at the user's head

Answer to Problem 76QAP

Magnetic field does the dryer produce at the user's head= $4866.67*{10}^{-7}\text{ T}$

  $\frac{B}{B_{earth}}=\frac{4866.67*{10}^{-7}\text{ T}}{5*{10}^{-5}\text{ T}}=9.73$

There's a possibility of health concerns due to the use of hair dryer

Explanation of Solution

Given info:

  $\begin{array}{l}\text{Voltage = }110\text{ V}\\ \text{Power = }1650\text{ W}\\ \text{Distance of the current from user head = }3\text{ cm}\\ {\text{Earth's magnetic field = 5*10}}^{\text{-5}}\text{ T}\end{array}$

Formula used:

  $\begin{array}{l}P=\frac{V^2}{R}\\ V=\text{potential}\\ P=\text{Power}\\ R=\text{resistance}\end{array}$

  $\begin{array}{l}B=\frac{{\mu }_{0}I}{2\pi d}\\ B=\text{Magnetic field}\\ {\mu }_0=\text{permeability of free space}\\ I=\text{Current in wire}\\ d=\text{Radius from the wire}\end{array}$

  $\begin{array}{l}V=IR\\ V=\text{potential}\\ I=\text{Current in wire}\\ R=\text{resistance}\end{array}$

Calculation:

  $\begin{array}{l}B=\frac{{\mu }_{0}I}{2\pi d}\\ B=\frac{4\pi *{10}^{-7}*7.3}{2\pi *3*{10}^{-3}}\\ B=4866.67*{10}^{-7}\text{ T}\end{array}$

Comparison with Earth's magnetic field,

  $\frac{B}{B_{earth}}=\frac{4866.67*{10}^{-7}\text{ T}}{5*{10}^{-5}\text{ T}}=9.73$

There's a possibility of health concerns due to the use of hair dryer

Conclusion:

Magnetic field does the dryer produce at the user's head= $4866.67*{10}^{-7}\text{ T}$

  $\frac{B}{B_{earth}}=\frac{4866.67*{10}^{-7}\text{ T}}{5*{10}^{-5}\text{ T}}=9.73$

There's a possibility of health concerns due to the use of hair dryer