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Chapter 31: Q. 29 (page 902)

What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle $CW$ or $cCW$ from vertical.

Short Answer

Expert verified

The force, $F_{B} = 1.6 脳 10^{鈭� 13} N$

The force, $F_{e} = 1.6 脳 10^{鈭� 13} N$

The net force, $F_{n e t} = 2.26 脳 10^{鈭� 13} N$

Step by step solution

01

Find the direction of electrostatic force.

With in presence of an electric field, there is an electrostatic force called $F_{E}$ .

02

Find FB, Fe, Fnet

The magnetic force flows north and use the right - hand principle.

Calculate $F_{B}$

localid="1648970948872" $\begin{aligned} F_{B} = q v B \end{aligned}$

$F_{B} = 1.6 脳 10^{鈭� 19} 脳 10^{7} 脳 0.1$ ( enter the quantities in the formula)

$F_{B} = 1.6 脳 10^{鈭� 13} N$

Calculate localid="1648971852105" $F_{e}$

localid="1648971000005" $F_{e} = e E$

$F_{e} = 1.6 脳 10^{鈭� 19} 脳 10^{鈭� 6}$ ( enter the quantities in the formula)

$F_{e} = 1.6 脳 10^{鈭� 13} N$

Calculate $F_{n e t}$

localid="1648971062338" $F_{n e t} = \sqrt{F_{B}^{2} + F_{e}^{2}}$

$F_{n e t} = \sqrt{2} 脳 F_{B}$

$F_{n e t} = \sqrt{2} 脳 1.6 脳 10^{鈭� 13}$ ( enter the quantities in the formula)

$F_{n e t} = 2.26 脳 10^{鈭� 13} N$

03

Find direction and θ

To find the direction and $胃$

$\tan 鈦� 胃 = \frac{F_{B}}{F_{e}}$

$\tan 鈦� 胃 = \frac{1.6 脳 10^{鈭� 13}}{1.6 脳 10^{鈭� 13}}$ ( enter the quantities in the formula)

$\tan 鈦� 胃 = 1 鈬� 胃 = 45^{鈭�}$

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d. Find an expression for the magnetic field strength as a function of time at a distancelocalid="1649879597467" $r > R$ from the center. Evaluate the magnetic field strength at localid="1649879602321" $r = 4.0 m m$ , localid="1649879607075" $t = 2.0 s$ .

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