Answer :
Answer:
The i component of F is 7963.2 x 10⁻¹⁹ N.
The j component of F is 4561.2 x 10⁻¹⁹ N.
The k component of F is -151.2 x 10⁻¹⁹ N.
Magnitude of force is 9178.05 x 10⁻¹⁹ N.
Magnitude of force in presence of electric field is 27483.91 x 10⁻¹⁹ N.
Explanation:
Lorentz Force is defined as the force experience by charge particle in presence of electric and magnetic field. It is given by :
F = q ( v x B + E ) .....(1)
Here F is force, v is velocity of particle , B is magnetic field and E is electric field all are in vector notation and q is charge of the particle.
In first case, given :
E = 0
q = 24 x 10⁻¹⁹ C
v = [(-3.68)i + (6.35)j + (-1.91)k] x 105 m/s
B = [(-3.05)i + (5.28)j + (-1.09)k] T
Force, F = q x (v x B )
Substitute the suitable values in the above equation.
[tex]F = 24\times10^{-19}\times \left[\begin{array}{ccc}i&j&k\\-3.68&6.35&-1.91\\-3.05&5.28&-1.09\end{array}\right]\times105[/tex]
F = 24 x 10⁻¹⁹ x { [6.35 x (-1.09) - (-1.91) x (5.28)] i - [(-3.68) x (-1.09) - (-1.91) x (-3.05)] j + [(-3.68) x (5.28) - 6.35 x (-3.05) ] k } x 105
F = 24 x 10⁻¹⁹ x 105 x [(3.16)i + (1.81)j + (-0.06)k] N ....(2)
The i component of F is 7963.2 x 10⁻¹⁹ N.
The j component of F is 4561.2 x 10⁻¹⁹ N.
The k component of F is -151.2 x 10⁻¹⁹ N.
Magnitude of force, F =[tex]\sqrt{(7963.2\times10^{-19}) ^{2} +(4561.2\times10^{-19}) ^{2} +(-151.2\times10^{-19}) ^{2} }[/tex]
F = 9178.05 x 10⁻¹⁹ N
In this case , E is also present and is equal to [(5.94)i + (-3.97)j + (-5.55)k] x 105 N/C. From equation (1) and (2) ;
F = 24 x 10⁻¹⁹ x [(3.16)i + (1.81)j + (-0.06)k + (5.94)i + (-3.97)j + (-5.55)k] x 105
F = 24 x 10⁻¹⁹ x 105 x [(9.1)i + (-2.16)j + (-5.61)k]
Magnitude of force, F = [tex]24\times10^{-19}\times105\times\sqrt{9.1^{2}+(-2.16^{2})+(-5.61^{2}) }[/tex]
F = 27483.9 x 10⁻¹⁹ N