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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Main 2023 · 24 January · Morning Shift · Physics · Magnetic Effects of Current

Two long straight wires P and Q carrying equal current 10A each...

Two long straight wires PP and QQ carrying equal current 10A10A each were kept parallel to each other at 5cm5cm distance. Magnitude of magnetic force experienced by 10cm10cm length of wire PP is F1{F}_{1}. If distance between wires is halved and currents on them are doubled, force F2{F}_{2} on 10cm10cm length of wire PP will be:

Options

  1. A8F18{F}_{1}
  2. B10F110{F}_{1}
  3. CF18\dfrac{{F}_{1}}{8}
  4. DF110\dfrac{{F}_{1}}{10}

Correct answer

A. 8F18{F}_{1}

Step-by-step solution

As we know, force per unit length between two parallel straight wires is given by, F=μ0i1i22\pidF = \dfrac{{\mu}_{0}{i}_{1}{i}_{2}}{2\pid}.

Therefore, required ratio

F1F2=μ0(10)22π(5×10−2)μ0(20)22π(52×10−2)=18\dfrac{{F}_{1}}{{F}_{2}} = \dfrac{\dfrac{{\mu}_{0} ( 10{)}^{2}}{2\pi ( 5 \times {10}^{- 2} )}}{\dfrac{{\mu}_{0} ( 20{)}^{2}}{2\pi\left(\dfrac{5}{2} \times {10}^{- 2}\right)}} = \dfrac{1}{8}

⇒F2=8F1⇒ {F}_{2} = 8{F}_{1}

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