A positively charged particle, having charge q, is accelerated by a potential difference V. This particle moving along the x-axis enters a region where an electric field E exists. The direction of the electric field is along positive y-axis. The electric field exists in the region bounded by the line $x = 0$ and $x = a$ . Beyond the line $x = a$ (i.e., in the region $x > a$ ), there exists a magnetic field of strength B, directed along the positive y-axis. Find the pitch of the helix formed after the particle enters the region $x \geq a$ . (Mass of the particle is m)

Open in App

Solution

Now, velocity of the particle as it crosses the line $x = a$
$\to v = {(\frac{2 q V}{m})}^{1 / 2}^i + \frac{q E}{m} {(\frac{2 q V}{m})}^{1 / 2}^j$
Magnetic field in this region, $\to B = B \to j$
Hence, the time period of revolution, $t = \frac{2 π m}{q B}$
Pitch, $P = v_{∥} t = \frac{2 π m}{m q B} \times a E {(\frac{m q}{2 V})}^{1 / 2}$
$P = \frac{π a E}{B} {(\frac{2 m}{V q})}^{1 / 2}$

Suggest Corrections

Similar questions

Q. A positively charged particle, having charge q, is accelerated by a potential difference V. This particle moving along the x-axis enters a region where an electric field E exists. The direction of the electric field is along positive y-axis. The electric field exists in the region bounded by the line

x = 0

and

x = a

. Beyond the line

x = a

(i.e., in the region

x > a

), there exists a magnetic field of strength B, directed along the positive y-axis. Find
at which point does the particle meet the line

x = a

Q. A positively charged particle, having charge q, is accelerated by a potential difference V. This particle, moving along the x-axis, enters a region where a constant electric field E exists. The direction of electric field is along positive y-axis. The electric field E exists in the region bounded by the lines x = 0 and x = a. Beyond the line x = a (i.e., in region x

\geq

a), there exists a constant magnetic field of strength B, directed along positive y-axis. What is the pitch of helix formed after particle enters the region x

\geq

a? (mass of the particle is m).

A particle of charge q and mass m moving with velocity v along the x - axis enters the region x>0 with uniform magnetic field B along positive z direction. The particle will penetrate in this region along x - axis up to a distance d equal to

Q. A positively charged particle moving along x-axis with a certain velocity enters a uniform electric field directed along positive y-axis. Its :

Join BYJU'S Learning Program

Now, velocity of the particle as it crosses the line x=a→v=(2qVm)1/2^i+qEm(2qVm)1/2^jMagnetic field in this region, →B=B→jHence, the time period of revolution, t=2πmqBPitch, P=v∥t=2πmmqB×aE(mq2V)1/2P=πaEB(2mVq)1/2