Question

two charged particles of charge ratio 1:4 moving with same velocity enter a region of uniform magnetic field of strength B and get deflected and move along curves with equal radius r ratio of their masses

Answer 1

Radius of the Path in Magnetic Field is given by

$r = \frac{mv}{qB}$

where m is the mass of the partice, v= velocity, q= charge
 and B= Magnetic Field

In this Question
  v₂=v₁
  4q₁=q₂
  r₁=r₂

=>   m₁v₁/Bq₁ = m₂v₂/Bq₂
=>   m₁/m₂ = 1:4

So, the ratio of the masses is 1:4

Answer 2

Answer:

The ratio of the masses of the charges is 1:4.

Explanation:

Given -
Charge ratio of the 2 particles - 1:4
Magnetic field strength - B
The radius of the path of magnetic field - r

To find - the ratio of masses of the charge

Formula - $r = \frac{mv}{qB}$

Solution -
We have been given that the velocities of the charges are the same, i.e., $v_1 = v_2$.
Next, we are given the ratio of the charges to be 1:4, i.e., $4q_1 = q_2$.
We are also given the radii of the 2 charges to be the same, i.e., $r_1 = r_2$

Now, we can replace the values of the radii using the given formula.

$\frac{m_1v_1}{q_1B_1} = \frac{m_2v_2}{q_2B_2}\\\\ \frac{m_1}{q_1} = \frac{m_2}{4q_1B_2}\\\\m_1 = \frac{m_2}{4B_2}\\\\\\\therefore \frac{m_1}{m_2} = \frac{1}{4}$

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