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QJEEM18Phe9ec: JEE Main 2018 Physics - Class 12 JEEM18Phe9ec Solution: A Helmholtz coil has a pair of loops, each with turns and…

A Helmholtz coil has a pair of loops, each with NN turns and radius RR . They are placed coaxially at distance RR and the same current I{\rm I} flows through the loops in the same direction. P,P, midway between the centers AA and CC , is given by [Refer to figure given below] :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Magnetic Effect of Current Question 176 English

Multiple Choice Options

  • A 8Nμ0I51/2R{{8N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}
  • B 8Nμ0I53/2R{{8N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}
  • C 4Nμ0I51/2R{{4N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}
  • D 4Nμ0I53/2R{{4N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}

Step-by-Step Verified Solution

P is the mid-point of line AC. A and C are the center of the two circle of each radius R.

Current flows through loop A and B are in same direction, So the magnetic field will also be in the same direction. Magnitude of magnetic field at paint P

= magnitude of magnetic field due to A and B at paint P.

= 2 [μ0NI R22(R2+R24)32]\left[ {{{{\mu _0}NI\,{R^2}} \over {2{{\left( {{R^2} + {{{R^2}} \over 4}} \right)}^{{3 \over 2}}}}}} \right]

== μ0 NIR2532R38{{{\mu _0}\,NI{R^2}} \over {{{{5^{{3 \over 2}}}{R^3}} \over 8}}}

= 8 μ0NI532 R{{8\,{\mu _0}NI} \over {{5^{{3 \over 2}}}\,R}}

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