Magnetic Field Due to Circular Current Carrying Wire

Practice Questions:

Question 1: moderate

An otherwise infinite, straight wire has two concentric loops of radii a and b carrying equal
currents in opposite directions as shown. The magnetic field at the common centre is zero for

1. \[\frac{a}{b}=\frac{\pi+1}{\pi}\]

2. \[\frac{a}{b}=\frac{\pi}{\pi+1}\]

3. \[\frac{a}{b}=\frac{\pi-1}{\pi+1}\]

4. \[\frac{a}{b}=\frac{\pi+1}{\pi-1}\]

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Question 2: moderate

A wire loop is formed by joining two sections of radii r1 and r2 subtending an angle θ at O. The magnetic field at O is B0.

1. \[B_{0}=\frac{\mu_{0}I}{4\pi}\left( \frac{1}{r_{1}}+\frac{1}{r_{2}} \right)\theta : outwards\]

2. \[B_{0}=\frac{\mu_{0}I}{4\pi}\left( \frac{1}{r_{1}}-\frac{1}{r_{2}} \right)\theta : inwards\]

3. \[B_{0}=\frac{\mu_{0}I}{2\pi}\left( \frac{1}{r_{1}}+\frac{1}{r_{2}} \right)\theta : outwards\]

4. \[B_{0}=\frac{\mu_{0}I}{2\pi}\left( \frac{1}{r_{1}}-\frac{1}{r_{2}} \right)\theta : inwards\]

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Question 3: difficult

Three rings, each having equal radius R, are placed mutually perpendicular to each other
and each having its centre at the origin of coordinate system. If current I is flowing thriugh
each ring then the magnitude of the magnetic field at the common centre is

1. \[\sqrt{3}\frac{\mu_{0}I}{2R}\]

2. Zero

3. \[\left( \sqrt{2}-1 \right)\frac{\mu_{0}I}{2R}\]

4. \[\left( \sqrt{3}-\sqrt{2} \right)\frac{\mu_{0}I}{2R}\]

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Question 4: moderate

A charge Q is uniformly distributed over the surface of non-conducting disc of radius R. The
disc rotates about an axis perpendicular to its plane and passing through its centre with an
angular velocity ω. As a result of this rotation a magnetic field of induction B is obtained at
the centre of the disc. If we keep both the amount of charge placed on the disc and its
angular velocity to be constant and vary the radius of the disc then the variation of the
magnetic induction at the centre of the disc will be represented by the figure

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Question 5: difficult

In the given figure the magnitude of magnetic field at O is (all three wires are quarter circular arc)

1. \[\frac{\mu_{0}I}{4R}\sqrt{3}\]

2. \[\frac{\mu_{0}I}{2R}\sqrt{3}\]

3. \[\frac{\mu_{0}I}{8R}\sqrt{3}\]

4. none of these

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Question 6: moderate

A current I is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is (MA = R, MB = 2R, angle DMA = 90°)

1. \[\frac{7\mu_{0}i}{16R}\] , but out of the plane of the paper.

2. \[\frac{5\mu_{0}i}{16R}\] , but out of the plane of the paper.

3. \[\frac{7\mu_{0}i}{16R}\] , but into the plane of the paper.

4. \[\frac{5\mu_{0}i}{16R}\] , but into the plane of the paper.

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Question 7: difficult

A current I flows around a closed path in the horizontal plane of the circle as shown in the figure. The path consists of eight arcs with alternating radii r and 2r. Each segment of arc subtends equal angle at the common centre P. The magnetic field produced by current path at point P is

1. \[\frac{3}{8}\frac{\mu_{0}I}{R}\] ,perpendicular to the plane of the paper and directed inward.

2. \[\frac{3}{8}\frac{\mu_{0}I}{R}\] , perpendicular to the plane of the paper and directed outward.

3. \[\frac{1}{8}\frac{\mu_{0}I}{R}\] , perpendicular to the plane of the paper and directed inward.

4. \[\frac{1}{8}\frac{\mu_{0}I}{R}\] , perpendicular to the plane of the paper and directed outward.

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Question 8: easy

A length of wire carries a steady current. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is :

1. a quarter of its first value

2. unaltered

3. four times of its first value

4. half of its first value

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Question 9: moderate

A coil having N turns is would tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at its centre is :

1. \[\frac{\mu_{0}NI}{b}\]

2. \[\frac{2\mu_{0}NI}{a}\]

3. \[\frac{\mu_{0}NI}{2\left( b-a \right)}log\frac{b}{a}\]

4. \[\frac{\mu_{0}NI}{\left( b-a \right)}log\frac{b}{a}\]

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Question 10: moderate

A particle carrying a charge equal to 100 times the charge on an electron is rotating per second in a circular path of radius 0.8m. The value of the magnetic field produced at the centre will be : (μ0 = permeability constant)

1. \[10^{-7}/\mu_{0}\]

2. \[10^{-17}\mu_{0}\]

3. \[10^{-6}/\mu_{0}\]

4. \[10^{-7}\mu_{0}\]

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