Respuesta :
Answer: [tex]0.985\times 10^{-4}\ T[/tex]
Explanation:
Given
Electron is accelerated 3.5 kV potential difference
Distance between plates d=29 mm
The potential difference between plates is V=100 V
here, the kinetic energy of an electron is acquired through a potential difference of 3.5 kV
[tex]\Rightarrow \dfrac{1}{2}m_ev^2=e\times 3.5\times 10^3\\\\\Rightarrow v=\sqrt{\dfrac{2\times 3.5\times 10^3e}{m_e}}=\sqrt{\dfrac{7\times 10^3\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}}\\\\\Rightarrow v=\sqrt{1.23\times 10^{15}}=3.5\times 10^7\ m/s[/tex]
To move in a straight line Force due to magnetic field must be balanced by force due to charge
[tex]\Rightarrow F_B=F_q\\\\\Rightarrow evB=eE\\\\\Rightarrow B=\dfrac{E}{v}\\\\\Rightarrow B=\dfrac{\frac{V}{d}}{3.5\times 10^7}=\dfrac{\frac{100}{0.029}}{3.5\times 10^7}\\\\\Rightarrow B=\dfrac{3.448\times 10^3}{3.5\times 10^7}=0.985\times 10^{-4}\ T[/tex]
