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Grade 11Magnetism

Ques.: A rod of length 'l' rotates with a small but uniform angular velocity about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is :
Answer: 1/8(B l^2) [Reference: H.C.Verma II
Though I've calculated the answer correct by Integration method,
but can anyone please solve this step by step by proceeding from this method -
(mv^2)/r = F(B) - F(E)
=> (mv^2)/r = evB - eE
=> mr^2 = erB - e 2 V / l ............. ????
Can anyone plzzz...

Profile image of Simran Bhatia
12 Years agoGrade 11
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1 Answer

Profile image of ROSHAN MUJEEB
5 Years ago
et us consider a small elementdxat a distancexfrom the centre of the rod rotating with angular velocityωabout its perpendicular bisector. The emf induced in the rod because of this small element is given by
de=Bvl=Bωxdxde=Bvl=Bωxdx

The emf induced across the centre and end of the rod is given by
∫de=∫l/20Bωxdx⇒E=Bω[x22]l/20⇒E=18Bωl2