A uniform wire of diameter d carries a current of 100 mA when the mean drift velocity of electrons in the wire is v. For a wire of diameter d/2 of the same material to carry a current of 200 mA, the mean drift velocity of electrons will be:
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Question

A uniform wire of diameter d carries a current of 100 mA when the mean drift velocity of electrons in the wire is v. For a wire of diameter d/2 of the same material to carry a current of 200 mA, the mean drift velocity of electrons will be:

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G1 Physics · Accepted Answer

Step 1: Current I = neAv(drift), keeping electron density n unchanged. Step 2: Halving diameter makes area A′ = A/4. Step 3: I′/I = 2 = (A′/A)(v′/v) = (1/4)(v′/v). Hence v′ = 8v.