If a second particle, with the same electric charge but ten times as massive, enters the field with the same velocity v ⃗, what is its period? View Available Hint (s) If a second particle, with the same electric charge but ten times as massive, enters the field with the same velocity, what is its period? T/10 T 5T 10T Submit Part B Complete previous part (s) Provide Feedback Next

When an moving electric charge passes through a uniform magnetic field

its motion becomes circular.

If m be the mass v be the velocity, q be the charge on the mass B be the magnetic field and R be the radius of circular path

force on the moving charge created by magnetic field

= B q v

Centripetal force required for circular motion

= m v² / R

For balancing

B q v = m v² / R

v = B q R / m

Time period of rotation

T = 2π R / v

= 2 π R m / B q R

= 2 π m / B q

For first particle

T₁ = 2 π m₁ / B q₁

For second particle

T₂ = 2 π m₂ / B q₂

q₁ = q₂ and 10 m₁ = m₂ (given)

Putting the values in second equation

T₂ = 2 π 10 m₁ / B q₁

= 10 x 2 π m₁ / B q₁

= 10 T₁

Given T₁ = T

T₂ = 10 T