VITEEE 2015 Paper

Torque when the wire is brought in a uniform field E.
τ = qEL sin θ
= qELθ [Since θ is very small]
Moment of inertia of rod AB about O
I = m(

L

2

)2+m(

L

2

)2 =

mL2

2

∴ α =

τ

l

=

qELθ

mL2 2

⇒ ω2θ =

2qELθ

mL2

[Since θ = ω2θ]
⇒ ω2 =

2qE

mL

Time period of the wire
T =

2π

ω

= 2π √

mL

2qE

The rod will become parallel to the field in time

T

4

∴ t =

T

4

=

π

2

√

mL

2qE