A charged particle is projected into a region containing a uniform magnetic field B = 0.5 j T. The initial velocity of the particle is v = (3 i + 4 j ) 10^3 m/s. The particle completes 5 revolutions while covering a distance of 8 cm along the y-axis. If the specific charge ( q/m ) of the particle is x 10^5 C/kg, the value of x is ________.

Step-by-step solution

Given: Velocity, v = (3 i + 4 j ) 10^3 m/s Magnetic field, B = 0.5 j T Number of revolutions, n = 5 Distance along y-axis, d = 8 cm = 0.08 m The component of velocity parallel to the magnetic field is v_ = 4 10^3 m/s. The time period of one revolution is: T = 2 m qB The total distance covered along the magnetic field in n revolutions is: d = n v_ T Substituting the expression for T : d = n v_ 2 m qB Rearranging to find the specific charge ( q/m ): q m = n v_ 2 d B Substituting the given values: q m = 5 4 10^3 2 0.0