two parallel coaxial circular coils of equal radius R and equal no of turns N carry equal currents I in the same direction and are represented by a distance 2R. find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

Question

Vikas TU · Answer

. Radius of 2 parallel co-axial circular coil = R Number of turns = N Current in both coils = I Distance between the 2 coils = 2R As the point where we have to find the magnetic field is half way between the 2 coils, it will be at a distance of R from center of both the coils. So the magnetic field at the point because of coil 1 = B1 So, B1 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 Similarly, B2 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 So, the total magnetic field, B = B1 + B2 B = B1 + B2 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 + (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 = (μ o NIR 2 ) / [(R+R) 2 +R] 3/2 = (μ o NIR 2 ) / [4R 2 +R] 3/2 = (μ o NIR 2 ) /8R 3 [1+1/R] 3/2 Since, R>>1 we can say B = (μ o NIR 2 ) /8R 3

Kushagra Madhukar · Answer

Dear student, Please find the solution to your problem. Radius of 2 parallel co-axial circular coil = R Number of turns = N Current in both coils = I Distance between the 2 coils = 2R As the point where we have to find the magnetic field is half way between the 2 coils, it will be at a distance of R from center of both the coils. So the magnetic field at the point because of coil 1 = B1 So, B1 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 Similarly, B2 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 So, the total magnetic field, B = B1 + B2 B = B1 + B2 = (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 + (μ o NIR 2 ) / 2[(R+R) 2 +R] 3/2 = (μ o NIR 2 ) / [(R+R) 2 +R] 3/2 = (μ o NIR 2 ) / [4R 2 +R] 3/2 = (μ o NIR 2 ) /8R 3 [1+1/R] 3/2 Since, R>>1 we can say B = (μ o NIR 2 ) /8R 3 Thanks and regrads, Kushagra

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two parallel coaxial circular coils of equal radius R and equal no of turns N carry equal currents I in the same direction and are represented by a distance 2R. find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

two parallel coaxial circular coils of equal radius R and equal no of turns N carry equal currents I in the same direction and are represented by a distance 2R. find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

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