Two wires $2 \mathrm{~mm}$ apart supply current to a $100 \mathrm{~V}$, $1 \mathrm{~kW}$ heater. The force…

Two wires $2 \mathrm{~mm}$ apart supply current to a $100 \mathrm{~V}$, $1 \mathrm{~kW}$ heater. The force per metre between the wires is $\left(\mu_0=4 \pi \times 10^{-27}\right.$ SI unit)
  1. $2 \times 10^{-2} \mathrm{~N}$
  2. $4 \times 10^{-3} \mathrm{~N}$
  3. $2 \times 10^2 \mathrm{~N}$
  4. $10^{-2} \mathrm{~N}$

Solution

Given: $P=1 \mathrm{~W}=1000 \mathrm{~W}, \mathrm{~V}=100 \mathrm{~V}$ $\therefore \quad \mathrm{I}=10 \mathrm{~A} \quad \ldots .(\because \mathrm{P}=\mathrm{VI})$ $\therefore \quad \mathrm{F}=\frac{\mu_0 \mathrm{I}_1 \mathrm{I}_2}{2 \pi \times \mathrm{a}}=\frac{4 \pi \times 10^{-7} \times 100}{2 \pi \times\left(2 \times 10^{-3}\right)}=10^{-7} \times 10^5=10^{-2} \mathrm{~N}$ ^

Asked in: MHT CET 2023 (10 May Shift 2)

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