Complete Question
The complete question is shown on the first uploaded image
Answer:
The acceleration would be [tex]a = 0.003* 6 =0.018\ m/s^2[/tex]
Explanation:
The objective of this solution is to obtain the acceleration of the particle
Now looking at Newton law which is mathematically represented as
[tex]F = ma[/tex]
Where F is the force experience by a particle
m is the mass of the particle
a is the acceleration of the particle
And also this force is equivalent to magnetic force in a magnetic field which is mathematically represented as
[tex]F = qvB[/tex]
Where q is the charge of the particle
v is the velocity of the charge
B is the magnetic field the charge is under it influence
Now equating this two formulas
[tex]ma = qvB[/tex]
Making a the subject we have
[tex]a = \frac{qvB}{m}[/tex]
In the question the direction of the is in the positive x-axis which is [tex]i[/tex] hence the direction would be in the [tex]i[/tex] direction
So substituting [tex](2.0i +3.0j+4.0k)mT = (2.0i +3.0j+4.0k)*10^{-3}T[/tex] for B
[tex]a = \frac{q}{m} * v (2.0i +3.0j +4.0k)*10^{-3}[/tex]
Substituting [tex]3.0 Km /s = 3.0*10^{3}\ m/s[/tex] for v and [tex]-6.0 \muC = -6.0*10^{-6} C[/tex] for q
[tex]a = \frac{-6.0*10^{-6}}{2.0*10^{-3}} * 3.0*10^{3} *(2i+3j+4k) *10^{-3}[/tex]
[tex]a = 0.003 * 3i(2i+3j+4k)[/tex]
[tex]a = 0.003 *((3*2)i \ \cdot i \ +(3*3) i \ \cdot \ j \ + (3*4)i \ \cdot \ k)[/tex]
According to vector multiplication
[tex]i \cdot i = j \cdot j = k\cdot k = 1\\\\and \ i\cdot j = i\cdot k = 0[/tex]
So
[tex]a = 0.003* 6 =0.018\ m/s^2[/tex]
