A particle of specific charge alpha enters a uniform magnetic field `B=-B_0hatk` with velocity `v=v_0hati` from the origin. Find the time dependence of velocity and position of the particle.
Text Solution
Verified by Experts
Velocity of the particle at ay time `t` is `v(t)=v_xhati+v_yhatj=v_0costhetahati+v_0sinthetahatj` or `v(t)=v_0cos(b_0alphat)hati+v_0sin(B_0alphat)hatj` Position of particle at `t` is `r(t)=xhati+yhatj=rsinthetahati+(r-rcostheta)hatj` substituting the values of `r` and `theta` we have `r(t)=v_0/(B_0alpha) [sin(B_0alphat)hati+(1-cos(B_(0))alphat))hatj]`
Topper's Solved these Questions
MAGNETICS
DC PANDEY ENGLISH|Exercise INTRODUCTORY EXERCISE|1 Videos
MAGNETICS
DC PANDEY ENGLISH|Exercise SUBJECTIVE_TYPE|1 Videos
MAGNETIC FIELD AND FORCES
DC PANDEY ENGLISH|Exercise Medical entrance s gallery|59 Videos
MAGNETISM AND MATTER
DC PANDEY ENGLISH|Exercise Medical gallery|1 Videos
Similar Questions
Explore conceptually related problems
A particle of spectfic charge alpha enters a uniform magnetic field B=-B_(0)hatk with velocity V=v_(0)hati from the origin Find the time dependence of velocity and position of the particle
A particle of specific charge alpha is projected from origin with velocity v=v_0hati-v_0hatk in a uniform magnetic field B=-B_0hatk . Find time dependence of velocity and position of the particle.
If a charged particle enters perpendicular in the uniform magnetic field then
A proton and an alpha -particles enters in a uniform magnetic field with same velocity, then ratio of the radii of path describe by them
A proton of charge e and mass m enters a uniform magnetic field B = Bi with an initial velocity v=v_xhati+v_yhatj . Find an expression in unit vector notation for its velocity at time t .
A charged particle enters a uniform magnetic field perpendicular to it. The magnetic field
A proton of charge +e and mass m enters a uniform magnetic Field vecB=hatB with an intial velocity vecv=v_(0x)hati+v_(0y)hatj . Find an expression in unit-vector notation for its velocity at any later time t.
A charge praticule of sepeific charge (charge/ mass ) alpha is realsed from origin at time t=0 with velocity v= v_(0)(hati+hatj) in unifrom magnetic fields B= B_(0)hati . Co-ordinaties of the particle at time t = (pi)/(B_(0)alpha) are
Assertion: A charged particle enters in a magnetic field B=B_0hati with velocity v=v_0hati+v_0hatj, then minimum speed of charged particle may be v_0 . Reason: A variable acceleration particle may be v_0 .
A particle of mass m and charge +q enters a region of magnetic field with a velocity v, as shown in Fig. 1.93. a. Find the angle subtended by the circular arc described by it in the magnetic field. b. How long does the particle stay inside the magnetic field? c. If the particle enters at E, what is the intercept EF?
