KVPY SA Exam 2016 Question Paper

Question : 28 of 80

Marks: +1, -0

An electric field due to a positively charged long straight wire at a distance r from it is proportional to

r ^{–1}

in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii 1 Å and 2 Å. The ratio of their respective time periods is

$1:1$
$1:2$
$2:1$
$4:1$

Validate

Solution:

E=K/r

∴F=qE

for 1st electron

(q)1/r_1={mv_1^2}/r_1

⇒q=mv_1^2

v_1^2=q/M

⇒v_1=√{q/M}

∴ Similarly

v_2=√{q/M}

v_1=v_2

T_1/T_2={{2nR_1}/v_1}/{{2nR_2}/v_2}

=R_1/v_1×v_2/R_2=1/2

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