If two charged particles projected with same speed have similar curved paths in a uniform perpendicular electrostatic field, then pick the false statements.

They have the same specific charges i.e., e/m.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Their masses must be same.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Their charges are of same polarity.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Magnitudes of their charges must be same.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
B Their masses must be same.
D Magnitudes of their charges must be same.

$y = \frac{1}{2} \frac{q E}{m} t^{2}$ ......( $1$ )

$x = u t$ .....( $2$ )

$y = \frac{q E}{2 m} \frac{x^{2}}{u^{2}} \Rightarrow y = (\frac{q}{m}) (\frac{E}{2 u^{2}}) x^{2}$

if they have similar paths then $\frac{q E}{2 m u^{2}}$ is same $\Rightarrow \frac{q_{1}}{m_{1}} = \frac{q_{2}}{m_{2}}$

so (b) and (d) are false.

Suggest Corrections

Similar questions

Q. Two particles of different masses

m_{1}

and

m_{2}

, different charges

Q_{1}

and

Q_{2}

, are accelerated through the same potential difference and then enter a uniform magnetic field in a direction perpendicular to the field. If they trace circular paths of same radius, then the ratio of their masses (

m_{1}

m_{2}

) must be :

Q. Two charged particles having charges

q_{1} a n d q_{2}

and masses

m_{1} a n d m_{2}

are projected with the same velocity in a region of uniform magnetic field. They follow the trajectory as shown

It can be concluded that

Q. Two charged particles having charges

q_{1}

and

q_{2}

and masses

m_{1}

and

m_{2}

are projected with same velocity in a region of uniform magnetic field. They follow the trajectory as shown in figure. From this, we can conclude that-

Two charged particles of masses $m$ and $3 m$ have charges $3 q$ and $q$ respectively. They are kept in a uniform electric field and allowed to move for the same time. The ratio of their kinetic energies is:

Q. Two charged particles of masses m and 2m have charges +2q and +q respectively. They are kept in a uniform electric field far away from each other and then allowed to move for the same time. Find the ratio of their kinetic energies.

Join BYJU'S Learning Program

If two charged particles projected with same speed have similar curved paths in a uniform perpendicular electrostatic field, then pick the false statements.

The correct options are B Their masses must be same. D Magnitudes of their charges must be same. y=12qEmt2......(1) x=ut.....(2) y=qE2mx2u2⇒y=(qm)(E2u2)x2 if they have similar paths then qE2mu2 is same ⇒q1m1=q2m2 so (b) and (d) are false.