Question

The acceleration of an electron at a certain moment in a magnetic field b=2 i +3j +4k is a = x i + j - k. Find the value of x is

Answer 1

value of x = 0.5

as we know, magnetic force, F = q(V × B) ,

where V is velocity of charged particle and B is magnetic field.

from formula, it is clear that F is perpendicular on magnetic field.

obviously, acceleration is also perpendicular upon magnetic field.

dot product of acceleration and magnetic field = 0

i.e., a.B = 0

⇒(2i + 3j + 4k).(xi + j - k) = 0

⇒2x + 3 - 4 = 0

⇒2x = 1

⇒x = 1/2 = 0.5

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c.i-3j+k

d.i+2j-2k

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Answer 2

Given: Magnetic field $b=2i+3j+4k$ and Acceleration $a=xi+j-k$

To Find: Find the value of $x$.

Step-by-step explanation:

Acceleration will be the same direction as force and force on a charged particle in a magnetic field is perpendicular to the field .

So,

Dot product of Acceleration and Magnetic field must be zero,

∴ $a.b=0$

⇒$(xi+j-k).(2i+3j+4k)=0$

⇒$2x+3-4=0$ (∵ $i.i=1,j.j=1\ and\ k.k=1$ )

⇒$2x=4-3$

⇒$x=\frac{1}{2}$

∴ $x=0.5$

So, The value of $x$ is $0.5$