Question 235: Magnetism and Matter

Question

A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarrow E $$ and $$\overrightarrow B $$ with a velocity $$\overrightarrow v $$ perpendicular to both $$\overrightarrow E $$ and $$\overrightarrow B, $$ and comes out without any change in magnitude or direction of $$\overrightarrow v $$. Then

Accepted Answer

Here, $$\overrightarrow E $$ and $$\overrightarrow B $$ are perpendicular to each other and the velocity $$\overrightarrow v $$ does not change; therefore
$$qE = qvB \Rightarrow v = {E \over B}$$
Also, $$\left| {{{\overrightarrow E  	imes \overrightarrow B } \over {{B^2}}}} ight| = {{E\,\,B\sin 	heta } \over {{B^2}}}$$
$$ = {{E\,\,B\sin {{90}^ \circ }} \over {{B^2}}} = {E \over B} = \left| {\overrightarrow v } ight| = v$$

Answer

$$\overrightarrow v  = \overrightarrow B  	imes \overrightarrow E /{E^2}$$

Answer

$$\overrightarrow v  = \overrightarrow E  	imes \overrightarrow B /{B^2}$$

Answer

$$\overrightarrow v  = \overrightarrow B  	imes \overrightarrow E /{B^2}$$

Answer

$$\overrightarrow v  = \overrightarrow E  	imes \overrightarrow B /{E^2}$$

Magnetism and Matter

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