Question

An electron moves straight inside a charged parallel plate capacitor of uniform surface charge density σ . The space, between the plates, has a constant magnetic field B, as shown in figure. Neglecting gravity, the time taken to cover straight line distance, ‘ l ’, by as electron, moving with a constant velocity v, in the capacitor, will be

(1) \(\frac{σ}{ε_0lB}\)

(2) \(\frac{σ}{ε_0B}\)

(3) \(\frac{ε_0lB}{σ}\)

(4) \(\frac{ε_0B}{σ }\)

Answer 1

 (3) \(\frac{ε_0lB}{σ}\)

Net electric field between the plates of capacitor

∴ Force on the electron due to electric field

|F_e| = eE

Force on the particle due to magnetic field

F_m = e(v x B) = evB

For unaccelerated straight line motion F_net = F_e + F_m = 0

Hence eE evB which gives v = E/B = σ/ε₀B

Hence, time of motion, inside the capacitor, is