Q=A particle having charge q=1C and mass m=1kg is released from rest at origin .There is an electric field E=(10 i^)N/C for 1.8 m and magentic field B=(-5 k^)T for 1.8 m

(a)=Find the time spent by the particle in the magnetic field region (in sec) .ans=(pie)/30 sec

The time spent by particle in magnetic field is given as

t_b = L/v_b =  2αm / qB

here,

L = length = 1.8m

v = velocity

and

α = angle 

m = mass

q = charge

B = magnetic field

now,

in electric field

F = qE = ma

or

m.(dv/dt) = qE

or

dv =  v - u = (qE/m).dt

as particle is initially at rest, u = 0

so,

v_e = (qE/m).t_e

and

also

t_e = L/v_e

or

v_e² = (qE/m).L

this will be the initial velocity of particle in magnetic field

now, we have

in magnetic field

F = ma = qvBsinα

m(dv/dt) = qvBsinα

dv_b = (qvBsinα / m).dt

assuming initially time is zero

dv_b = (qvBsinα / m).t_b

here,

t_b = L/v_b