In the region having mutually perpendicular electric and magnetic fields, a dielectric ball is attached to a thread of length l (see figure). Mass of the ball is m, charge q, the electric field E, magnetic field B. Find the period of small oscillations (in sec.) of the pendulum in a plane perpendicular to the magnetic field. (Take l=1 m , q =-1 μ C , E =7.5 V / m , m =1 mg , B =0.5 T )

Question

In the region having mutually perpendicular electric and magnetic fields, a dielectric ball is attached to a thread of length l (see figure). Mass of the ball is m, charge q, the electric field E, magnetic field B. Find the period of small oscillations (in sec.) of the pendulum in a plane perpendicular to the magnetic field. (Take l=1 m , q =-1 μ C , E =7.5 V / m , m =1 mg , B =0.5 T ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

mg - qE = mg eff g -( qE / m )= g eff T =2 π √(ℓ/ g - q ( E ) m ) ⇒ T =2 π √(1/10-(10-6 × 7.5)10-6)=4 sec

mg−qE=mgeff​ g−mqE​=geff​ T=2πg−qmE​ℓ​​ ⇒T=2π10−10−610−6×7.5​1​​=4sec

$m g - qE = m g_{e ff}$
$g - \frac{qE}{m} = g_{e ff}$
$T = 2 π \frac{ℓ}{g - q \frac{E}{m}}$
$\Rightarrow T = 2 π \frac{1}{10 - \frac{1 0 ^{- 6} \times 7.5}{1 0 ^{- 6}}} = 4 sec$