Question 210: Magnetism and Matter

Question

A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $$ 	imes $$ 10$$-$$19C)

Accepted Answer

Given,
radius of circular path(r) = 0.5 cm
Magnetic field (B) = 0.5 T
Electric field (E) = 100 V/m
Charge of particle (q) = 1.6$$ 	imes $$10
$$-$$19
C
As particle is moving in a circular path so,
$${{m{v^2}} \over r} = qvB$$
$$ \Rightarrow $$  r = $${{mv} \over {qB}}$$ . . . . . . . (1)
When electric field of 100 v/m is applied on the particle then particle is moving in the straight line. So, the net force on the particle is zero.
$$ 	herefore $$    F
net
= 0
$$ \Rightarrow $$   F
e
= F
m
$$ \Rightarrow $$  qE = qvB
$$ \Rightarrow $$   E = vB  . . . . .(2)
From equation (1) and (2) we get,
r = $${m \over {qB}}\left( {{E \over B}} ight)$$
= $${{mE} \over {q{B^2}}}$$
$$ \Rightarrow $$   m = $${{q{B^2}r} \over E}$$
=  $${{1.6 	imes {{10}^{ - 19}} 	imes {{\left( {0.5} ight)}^2} 	imes 0.5 	imes {{10}^{ - 2}}} \over {100}}$$
= 2 $$ 	imes $$ 10
$$-$$24
kg

Answer

9.1 $$ 	imes $$ 10$$-$$31 kg

Answer

1.6 $$ 	imes $$ 10$$-$$27 kg

Answer

1.6 $$ 	imes $$ 10$$-$$19 kg

Answer

2.0 $$ 	imes $$ 10$$-$$24 kg

Magnetism and Matter

A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $ \times 10-$19C)

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