An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field B . If speed of the electron is doubled and the magnetic f

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An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field B . If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

TestHub · Accepted Answer

In a perpendicular magnetic field, Magnetic force = centripetal force ie, ​ Bq v = r m v 2 ​ ⇒ r = Bq m v ​ ∴ r 2 ​ r 1 ​ ​ = v 2 ​ v 1 ​ ​ × B 1 ​ B 2 ​ ​ r 2 ​ r 1 ​ ​ = 2 1 ​ × 2 1 ​ r 2 ​ = 4 r 1 ​ ⇒ r 2 ​ = 4 r ​

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