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Force on a Straight Current Carrying Conductor Placed in a Magnetic Field

Two charged p...

Question

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

A

q_{1} > q_{2}

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B

q_{1} > q_{2}

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C

m_{1} > m_{2}

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D

m_{1} q_{2} < m_{2} q_{1}

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Solution

The correct option is D $m_{1} q_{2} < m_{2} q_{1}$
Let $r_{1} a n d r_{2}$ be the radius 1 and 2, respectively. Thus, according to the figure given in the question $r_{1} < r_{2} .$
Radius (r) of path of a charged particle (q) projected in a uniform magnetic field (B) with speed (v):
$r = \frac{m v}{q B}$
$\Rightarrow r \propto \frac{m}{q} [Since, v and B are same for both the charges]$
Now, $r_{1} < r_{2}$
$\Rightarrow \frac{m_{1}}{q_{1}} < \frac{m_{2}}{q_{2}}$
$\Rightarrow m_{1} q_{2} < m_{2} q_{1}$
Hence, the correct answer is option (4).

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