Question

Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of $8.46$ A circulating clockwise and has a radius of $6.20 \mathrm{~cm}$. The smaller loop has a radius of $4.42 \mathrm{~cm} .$ What is the current in the smaller loop if the total magnetic field at the center of the system is zero? [See Eq. (19-16).]

          Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of $8.46$ A circulating clockwise and has a radius of $6.20 \mathrm{~cm}$. The smaller loop has a radius of $4.42 \mathrm{~cm} .$ What is the current in the smaller loop if the total magnetic field at the center of the system is zero? [See Eq. (19-16).]
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of $8.46$ A circulating clockwise and has a radius of $6.20 \mathrm{~cm}$. The smaller loop has a radius of $4.42 \mathrm{~cm} .$ What is the current in the smaller loop if the total magnetic field at the center of the system is zero? [See Eq. (19-16).]
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Transcript

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00:02 So in this question actually it is said that there are two concentric loops.
00:06 Consentic loops, one loop is like this and another is also like this.
00:10 So they are having the same center.
00:12 So center is same.
00:13 Now what happens? since the magnetic field at the center is zero, what is magnetic field at the center? magnetic field at the center is zero.
00:20 So what we will do b1 is equal to b2.
00:23 That is magnetic field due to bigger loop is equal to due to lower loop.
00:28 Its magnitude will be equal.
00:30 So mod value of this will be equal.
00:32 Means they will be opposite in sign only because one will be attractive and one will be repulsing.
00:36 That is where the net magnetic field will be 0.
00:39 So how magnetic field in the center of the loop is given as mu not i1 upon 2 r1.
00:45 R1 is the radius of this one.
00:48 Let's say this is r1 and another is r2...
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