Question 188: Magnetism and Matter

Question

A charged particle carrying charge 1 $$\mu $$C is moving
with velocity $$\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$$ ms
–1
. If an external
magnetic field of $$\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$$× 10
–3
T exists in the region where the particle is moving then the
force on the particle is $$\overrightarrow F $$
 × 10
–9
N. The vector $$\overrightarrow F $$
is :

Accepted Answer

Given,
$${\overrightarrow V }$$ = $$\left( {2\widehat i + 3\widehat j + 4\widehat k} ight)$$ ms
Ã¢ÂÂ1
$${\overrightarrow B }$$ = $$\left( {5\widehat i + 3\widehat j - 6\widehat k} ight)$$ÃÂ 10
Ã¢ÂÂ3
T
q = 1 $$\mu $$C
$$\overrightarrow F  = q\left( {\overrightarrow V  	imes \overrightarrow B } ight)$$
= $${10^{ - 6}} 	imes {10^{ - 3}} 	imes \left| {\matrix{
   {\widehat i} & {\widehat j} & {\widehat k}  \cr 
   2 & 3 & 4  \cr 
   5 & 3 & { - 6}  \cr

} } ight|$$
= ($${ - 30\widehat i + 32\widehat j - 9\widehat k}$$) $$ 	imes $$ 10
-9

Answer

$${ - 0.30\widehat i + 0.32\widehat j - 0.09\widehat k}$$

Answer

$${ - 300\widehat i + 320\widehat j - 90\widehat k}$$

Answer

$${ - 30\widehat i + 32\widehat j - 9\widehat k}$$

Answer

$${ - 3.0\widehat i + 3.2\widehat j - 0.9\widehat k}$$

Magnetism and Matter

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