Question

A particle of charge q and mass m starts moving from origin under the action of an Electric field \[\overrightarrow E = {E_0}\overrightarrow i \]and magnetic field \[\overrightarrow B = {B_0}\overrightarrow k \]. Its velocity at $\left( {x,3,0} \right)$is $\left( {4i + 3i} \right)$, the value of x is:
A. $\dfrac{{36{E_0}{B_0}}}{{qm}}$
B. $\dfrac{{25m}}{{2q{E_0}}}$
C. $\dfrac{{10m}}{{q{E_0}}}$
D. $\dfrac{{25{E_0}{B_0}}}{m}$

Answer 1

Hint: The magnetic field vector is defined as the vector which represents the magnetic field strength in the magnitude and the direction at any point in a wave that is propagating. The magnitude of the electric field and the direction of the electric field are represented by the value of E which is called electric field or electric field strength.

Complete step by step answer:
Given data:
The Charge = q
The mass of the particle = m
Electric field, \[\overrightarrow E = {E_0}\overrightarrow i \]
The Magnetic field, \[\overrightarrow B = {B_0}\overrightarrow k \]
The velocity at $\left( {x,3,0} \right)$= $\left( {4i + 3i} \right)$
The value of x =?
We know that $\left( {q{E_0}x} \right) = \dfrac{1}{2}m{v^2}\_\_\_\_\_\_\_\_\_\left( 1 \right)$
On solving the velocity equation, we get, v = 25
Substituting the value of v in equation 1, we get,
$ \Rightarrow \left( {q{E_0}x} \right) = \dfrac{{25m}}{2}$
$ \Rightarrow x = \dfrac{{25m}}{{2q{E_0}}}$
Thus the value of $x = \dfrac{{25m}}{{2q{E_0}}}$

Hence, the correct answer is option (B).

Note:
1. The region around a magnet where the moving charge experiences a force is called a magnetic field. It depends on the magnet, the number of turns in the solenoid, the length of the solenoid, and the amount of the current flowing.
2. The Electric field will never be negative and is always positive. Inside a current-carrying conductor. The electric field is zero. The electric field will depend on the amount of the charge, the nature of the medium, and also on the distance which is radially away from the center of the source.
3. In general, electric fields originate from the electric charges or the magnetic fields. In general, the electric field near the charge will be high and goes on decreasing as we move farther away from the charge.