Question 205: Magnetism and Matter

Question

The region between y = 0 and y = d contains a magnetic field $$\overrightarrow B  = B\widehat z$$.  A particle of mass m and charge q enters the region with a velocity $$\overrightarrow v  = v\widehat i.$$ If d $$=$$ $${{mv} \over {2qB}},$$ the acceleration of the charged particle at the point of its emergence at the other side is :

Accepted Answer

Here R = $${{mv} \over {qB}}$$ = 2d
cos $$	heta $$ = $${{{R \over 2}} \over R}$$ = $${1 \over 2}$$
$$ \Rightarrow $$ $$	heta $$ = 60
o
Acceleration of the charged particle at the point of its emergence,
$$\overrightarrow {{a_c}}  = {a_{{c_x}}}\left( { - \widehat i} ight) + {a_{{c_y}}}\left( { - \widehat j} ight)$$
= $${a_c}\cos 30^\circ \left( { - \widehat i} ight) + {a_c}\sin 30^\circ \left( { - \widehat j} ight)$$
= $${a_c}\left( {{{\sqrt 3 } \over 2}\left( { - \widehat i} ight) + {1 \over 2}\left( { - \widehat j} ight)} ight)$$
= $${{qvB} \over m}\left( { - {{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} ight)$$

Answer

$${{qvB} \over m}\left( -{{{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} \right)$$

Answer

$${{qvB} \over m}\left( {{1 \over 2}\widehat i - {{\sqrt 3 } \over 2}\widehat j} \right)$$

Answer

$${{qvB} \over m}\left( {{{ - \widehat j + \widehat i} \over {\sqrt 2 }}} \right)$$

Answer

$${{qvB} \over m}\left( {{{\widehat j + \widehat i} \over {\sqrt 2 }}} \right)$$

Magnetism and Matter

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