Question : An alpha particle is projected with velocity V=(3.0×105) m/s i into a region in which magnetic field B=[(0.4T)i+(0.3T)j] exists. Calculate the acceleration of the particle in the region. i, j and k are unit vectors along x, y and z axis respectively and charge to mass ratio for alpha particles is 4.8×107 C/kg.
Doubt by Rohan
Solution :
V=(3.0×105) m/s i
B=[(0.4T)i+(0.3T)j]
Solution :
V=(3.0×105) m/s i
B=[(0.4T)i+(0.3T)j]
q/m = 4.8×107 C/kg
We know,
According to Magnetic Lorentz Force,
F=q(V×B)
ma=q(V×B)
a=(q/m)(V×B)
a=(q/m){[(3.0×105)i]×[(0.4T)i+(0.3T)j]}
a=(q/m){[(0.9×105)k]}
a=(4.8×107)(0.9×105)k
a=(4.32×1012)k m/s²
The acceleration is directed along the +z axis.
We know,
According to Magnetic Lorentz Force,
F=q(V×B)
ma=q(V×B)
a=(q/m)(V×B)
a=(q/m){[(3.0×105)i]×[(0.4T)i+(0.3T)j]}
a=(q/m){[(0.9×105)k]}
a=(4.8×107)(0.9×105)k
a=(4.32×1012)k m/s²
The acceleration is directed along the +z axis.
