91Ó°ÊÓ

$$\begin{gathered} \stackrel{→}{v}=\left(2.0×{10}^6\right)\stackrel{¯}{i}+\left(3.0×{10}^6\right)\hat{j} \\ \stackrel{→}{B}=\left(0.030\right)\hat{i}-\left(0.15\right)\hat{j} \end{gathered}$$

Find the magnetic force on the electron using the formula for magnetic force in terms of charge, magnetic field strength, and velocity of electron.

Formulae are as follow:

$\stackrel{→}{F_B}=e\stackrel{→}{v}×\stackrel{→}{B}$

Where, F_B is magnetic force, v is velocity, B is magnetic field, e is charge of particle.

The magnetic force experienced by the electron is,

$\stackrel{→}{F_B}=e\stackrel{→}{v}×\stackrel{→}{B}$

$F_B=\left(-1.6×{10}^{-19}\right)\left[\left(\left(2.0×{10}^6\right)\hat{i}+\left(3.0×{10}^6\right)\hat{j}\right)×\left(\left(0.030\right)\hat{i}-\left(0.15\right)\hat{j}\right)\right]$

$$\begin{gathered} \stackrel{→}{v}×\stackrel{→}{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2.0×{10}^6& 3.0×{10}^6& 0\\ 0.030& -0.15& 0\end{array}\right| \\ \stackrel{→}{v}×\stackrel{→}{B}=\left[\left(\left(2.0×{10}^6\right)\left(-0.15\right)\right)-\left(3.0×{10}^6\right)\left(0.030\right)\right]\hat{k} \\ \stackrel{→}{v}×\stackrel{→}{B}=\left(-0.39×{10}^6\right)\hat{k}\frac{m}{s}T \end{gathered}$$

Hence,

$$\begin{gathered} F_B=\left(-1.6×{10}^{-19}\right)\left(-0.39×{10}^6\right)\hat{k} \\ {F}_B=0.624×{10}^{-13}N\hat{k}~\left(6.2×{10}^{-14}N\right)\hat{k} \end{gathered}$$

Hence, the magnetic force experienced by the electron islocalid="1663047307015" $F_B=-0.624×{10}^{-13}N\hat{k}~\left(6.2×{10}^{-14}N\right)\hat{k}$

Since, proton will experience the same magnetic field, and its velocity is the same but charge on it is positive.

Therefore, the magnetic force experienced by proton is $F_B=-0.624×{10}^{-13}N\hat{k}~-6.2×{10}^{-14}N\hat{k}$

Hence, the magnetic force experienced by the proton is $F_B=-0.624×{10}^{-13}N\hat{k}~-6.2×{10}^{-14}N\hat{k}$

Therefore, the magnetic force on the electron and proton can be found using the formula for magnetic force in terms of charge, magnetic field strength, and velocity of electron.