Two ends of a current carrying wire AB of length l, radius r and resistivity of material ρ are connected to the terminals of a battery of emf E. The wire AB is placed in a uniform magnetic field of induction B→ as shown. Force experienced by the wire is $$20$$ N. It radius of the wire is doubled and length also doubled, force experienced by the wire will be

Question

Two ends of a current carrying wire AB of length l, radius r and resistivity of material ρ are connected to the terminals of a battery of emf E. The wire AB is placed in a uniform magnetic field of induction B→ as shown. Force experienced by the wire is $$20$$ N. It radius of the wire is doubled and length also doubled, force experienced by the wire will be

Infinity Learn · Accepted Answer

Current through the wire is given by $$i=ER=E$$ρ.$$l/$$π$$r2=E$$.π$$r2$$ρ.l⇒i∝$$r2lF=Bil$$∴F ∝$$r2$$ $$F1F=r1r2$$⇒$$F1=4$$×$$20$$  $$N=80$$  N

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