Question 189: Magnetism and Matter

Question

A particle of mass m and charge q has an initial velocity $$\overrightarrow v  = {v_0}\widehat j$$
. If an electric field $$\overrightarrow E  = {E_0}\widehat i$$
 and
magnetic field $$\overrightarrow B  = {B_0}\widehat i$$
 act on the particle, its speed will double after a time:

Accepted Answer

Electric field will increase the speed of particle in x direction.
F
x
= qE
$$ 	herefore $$ a = $${{qE} \over m}$$
Also v
x
= at = $${{qE} \over m}$$t
$$v_x^2 + v_y^2 = {v^2}$$
$$ \Rightarrow $$ $$v_x^2 + v_0^2 = {\left( {2{v_0}} ight)^2}$$
$$ \Rightarrow $$ v
x
= $$\sqrt 3 $$v
0
$$ 	herefore $$ $${{qE} \over m}$$t = $$\sqrt 3 $$v
0
$$ \Rightarrow $$ t = $${{\sqrt 3 m{v_0}} \over {q{E_0}}}$$

Answer

$${{3m{v_0}} \over {q{E_0}}}$$

Answer

$${{\sqrt 2 m{v_0}} \over {q{E_0}}}$$

Answer

$${{\sqrt 3 m{v_0}} \over {q{E_0}}}$$

Answer

$${{2m{v_0}} \over {q{E_0}}}$$

Magnetism and Matter

A particle of mass m and charge q has an initial velocity $\overrightarrow v = {v_0}\widehat j . If an electric field \overrightarrow E = {E_0}\widehat i and magnetic field \overrightarrow B = {B_0}\widehat i$ act on the particle, its speed will double after a time:

Choose the correct answer: