Question

Please help me thank you soo much

Answer 1

Let charged particle travelled d distance before entering in Magnetic field.

Initial velocity = Vo = 0

Finding Acceleration,
F = q E
ma = q V/d...........(1)

q = charge
m = mass
a = acceleration

Also using formula,
${v}^{2} = Vo {}^{2} + 2ad$
${v}^{2} = 2ad..........(2)$

Now, equating centrifugal force and magnetic force,

$\frac{m {v}^{2} }{r} = qvB$

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

$\frac{ m\sqrt{2ad} }{qB} = r.........from \: (2)$

$\frac{ m\sqrt{2( \frac{qv}{md} )d} }{qB} = r.........from \: (1)$

$\frac{ \sqrt{2( mqv)} }{qB} = r$

$r = \sqrt{ \frac{2mv}{q} } ( \frac{1}{B} )$

Option C.