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Question

A proton moving with a velocity V is acted upon by electric field E and magnetic field B. The proton will move undeflected if


A
E is perpendicular to B
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B
E is parallel to V and perpendicular to B
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C
E is parallel to B and both are perpendicular to V
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D
E, V and B are mutually perpendicular and V=E/B
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Solution

The correct option is B E, V and B are mutually perpendicular and $$V = E/B$$
Force due to magnetic field $$=$$Force due to electric field
$$q(\vec{V}\times \vec{B}) = q\vec{E}$$
$$\Rightarrow \vec{V}\times \vec{B} =  \vec{E}$$
So, E, V and B are mutually perpendicular and VB = E    $$(\because sin 90^0 = 1)$$
or $$V = \frac{E}{B}$$

Physics

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