A beam of particles, each with a charge of 24.0 x 10-19 C, moves at [ (-3.68)i + (6.35)j + (-1.91)k ] x 105 m/s through a uniform magnetic field of [ (-3.05)i + (5.28)j + (-1.09)k ] T. Let F represent the force vector on each particle.

What is the i component of F?
(include units with answer)

What is the j component of F?
(include units with answer)

What is the k component of F?
(include units with answer)

What is the magnitude of F?
(include units with answer)

A uniform electric field of [ (5.94)i + (-3.97)j + (-5.55)k ] x 105 N/C is added to the system. What is the new magnitude of F?
(include units with 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.

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 =

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 =

F = 27483.9 x 10⁻¹⁹ N

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

a sonic boom is a loud boom that breaks the sound barrier

explanation: