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CBSE Class 12 Physics 2017 Outside Delhi Set 1 Paper

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Question : 8 of 26
Marks: +1, -0
Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.
Solution:  
Condition
(i)For directions of E‾,B‾,v⃗\overline{E}, \overline{B}, \vec{v}
(ii)For magnitudes of E⃗,B⃗,v⃗\vec{E}, \vec{B}, \vec{v}
(i)The velocity v⃗\vec{v} , of the charged particles, and the E⃗\vec{E} and B⃗\vec{B} vectors, should be mutually perpendicular.
Also the forces on qq , due to E⃗\vec{E} and B⃗\vec{B}, must be oppositely directed.
(Also accept if the student draws a diagram to show the directions.)
(ii) qE=qvBqE = qvB
 or v=EB\text{ or } v = \frac{E}{B}
[Alternatively, The student may write : Force due to electric field =qE⃗= q \vec{E}
Force due to magnetic field =q(v⃗×B⃗)= q(\vec{v} \times \vec{B})
The required condition is
qE⃗=−q(v⃗×B⃗)q \vec{E} = -q(\vec{v} \times \vec{B})
 [or E⃗=−(v⃗×B⃗)=(B⃗×v⃗)\text{ [or } \vec{E} = -(\vec{v} \times \vec{B}) = (\vec{B} \times \vec{v})
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