Question

An experimenter's diary reads as follows A charged particle is projected in a magnetic field of (7.0 →i − 3.0 →j) × 10−3 T. The acceleration of the particle is found to be (□→i + 7.0 →j) × 10−6 m s−2." The number to the left of →i in the last expression was not readable. What can this number be?"

Answer 1

The number is $(3 i+7 j) \times 10^{-6} \mathrm{m} / \mathrm{s}^{2}$

Explanation:

Step 1:

In the equation, it is given that  

Magnetic field, $B=(-3.0 j+7.0 i) \times 10^{-3} \mathrm{T}$

Particle’s acceleration, $a=(x i+7 j) \times 10^{-6} \mathrm{m} / \mathrm{s}^{2}$

Step 2:

The unidentified number has been signified as x.

a and b are perpendicular to one other. This is due to the reason that the magnetic force acts perpendicular always to the particle’s motion.

Step 3:

Hence, the two quantities’ dot products must be zero.

That is, $\mathrm{B} \cdot a=0$

$\Rightarrow 7 x \times 10^{-3} \times 10^{-6}-3 \times 10^{-3} \times 7 \times 10^{-6}=0$

$x=217=3$

The particle’s acceleration is $(3 i+7 j) \times 10^{-6} \mathrm{m} / \mathrm{s}^{2}$