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Byju's Answer

Standard XII

Physics

Measuring Mass

In a certain ...

Question

In a certain region uniform electric field $\to E = - E_{o}^k$ and magnetic field $\to B = B_{o}^k$ are present. At time t=0 a particle of mass m and charge q is given a velocity $\to v = v_{o}^j + v_{o}^k$ .Find the minimum speed of the particle and the time when it happens so.

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Solution

$a_{E} = \frac{q E_{o}}{m}$ (along negative z-direction)
Electric field will make z-component of velocity zero.At that time speed of the particle will be minimum and that minimum speed is the other component i.e., $v_{o}$ .
This is minimum when:
$v_{z} = u_{z} + a_{z} i$
$0 = v_{o} - \frac{q E_{o}}{m} t$
$t = \frac{m v_{o}}{q E_{o}}$

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In a certain region uniform electric field →E=−Eo^k and magnetic field →B=Bo^k are present. At time t=0 a particle of mass m and charge q is given a velocity →v=vo^j+vo^k.Find the minimum speed of the particle and the time when it happens so.

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In a certain region uniform electric field $\to E = - E_{o}^k$ and magnetic field $\to B = B_{o}^k$ are present. At time t=0 a particle of mass m and charge q is given a velocity $\to v = v_{o}^j + v_{o}^k$ .Find the minimum speed of the particle and the time when it happens so.