Problem 15.23

a) กำหนดให้ \(m = 1.67\times 10^{-27} kg, q = +e = 1.60\times 10^{-19} C,\)

k̂î

\(|\vec{v}| = 1.50\times 10^{7} m/s, \vec{v} = |\vec{v}| , |\vec{a}| = 2.20\times 10^{13} m/s^{2}, \vec{a} = |\vec{a}|\)

îĵ

และ \(\vec{B} = B_{x}+ B_{y}\)

จาก \(\vec{F}_{B}= q\vec{v}\times \vec{B}\)

îĵk̂

î

\(m|\vec{a}|= e\)

\(00|\vec{v}|\)

\(B_{x}B_{y}0\)

îîĵ

\(m|\vec{a}|= -e|\vec{v}|B_{y}+ e|\vec{v}|B_{x}\)

\(\therefore m|\vec{a}| = -e|\vec{v}|B_{y}\)

\(B_{y}= -\frac{m|\vec{a}|}{e|\vec{v}|}= -0.0153 T\)

และ \(0 = e|\vec{v}|B_{x}\)

\(B_{x}= 0\)

ĵ

\(\therefore \vec{B} = -0.0153 T \;\blacksquare\)

b) จาก \(Σ\vec{F} = 0\)

\(\vec{F}_{E}+ \vec{F}_{B}= 0\)

\(e\vec{E} + e\vec{v}\times \vec{B} = 0\)

\(\vec{E} = -\vec{v}\times \vec{B}\)

\(\vec{E} = \vec{B}\times \vec{v}\)

îĵk̂

\(\vec{E} =\)

\(0-0.01530\)

\(001.50\times 10^{7}\)

î

\(\vec{E} = -2.30\times 10^{5} N/C \;\blacksquare\)