Question

A charged particle is projected in a magnetic field B =(3 i +4 j )×10-² T and the acceleration is found to be a =(3 i+x j)m/s 2. The value of x is :​

Answer 1

Answer:

here is your solution in attachment

Answer 2

$-\frac{9}{4}$ is the value of x in the acceleration equation.

Given:

Charged particle is projected in a magnetic field ,$\[B\text{ }=\left( 3\text{ }i\text{ }+4\text{ }j\text{ } \right)\times {{10}^{-2}}\text{ }T\]$

Acceleration is found to be $\[a\text{ }=\left( 3\text{ }i+x\text{ }j \right)\frac{m}{{{s}^{2}}}\]$

To Find:

The value of x

Explanation:

Magnetic Force on charged particles (q) moving with velocity (V) in magnetic field is given as

              $\[\overset{\to }{\mathop{F}}\,=q(\overset{\to }{\mathop{V}}\,\times \overset{\to }{\mathop{B}}\,\]$

Magnetic force is perpendicular to magnetic field.

             $\[ & \overset{\to }{\mathop{F}}\,\bot \overset{\to }{\mathop{B}}\, \\ & \overset{\to }{\mathop{F}}\,\centerdot \overset{\to }{\mathop{B}}\,=0 \\ \end{align}\]$

Magnetic force is defined as product of mass and acceleration.

            $\[ & \overset{\to }{\mathop{ma}}\,\bot \overset{\to }{\mathop{B}}\, \\ \\ & \overset{\to }{\mathop{a}}\,\centerdot \overset{\to }{\mathop{B}}\,=0 \\ \end{align}\]$

Substituting the acceleration and magnetic field in the equation.

           $\[(3i+xj)\centerdot (3i+4j)\]$

Dot product of the equation is,

           $9+4x=0$

            $x=-\frac{9}{4}$

Hence, The value of x is $-\frac{9}{4}$  .