01. Amperes Law (∞, Length, Solenoid, Toroid)
Moving Charges & Magnetism

153437 A $50 \mathrm{~cm}$ long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?

1 $10.5 \mathrm{~A}$
2 $12.5 \mathrm{~A}$
3 $25.0 \mathrm{~A}$
4 $20.0 \mathrm{~A}$
Moving Charges & Magnetism

153438 Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\left|\frac{\mathrm{B}_{X}}{\mathrm{~B}_{\mathrm{Y}}}\right|$ is

1 $1: 4$
2 $2: 1$
3 $1: 2$
4 $4: 1$
Moving Charges & Magnetism

153439 A solenoid of length $2 \mathrm{~m}$ carries a current of 20A. The diameter of the solenoid is $3 \mathrm{~cm}$. If the magnetic field inside the solenoid is $20 \mathrm{mT}$, then the length of wire forming the solenoid is (assume, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

1 $100 \mathrm{~m}$
2 $125 \mathrm{~m}$
3 $175 \mathrm{~m}$
4 $150 \mathrm{~m}$
Moving Charges & Magnetism

153445 Consider a circular loop of radius $R$ on the $x-y$ plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by

1 $\frac{\mu_{0}}{2 R} I \hat{x}$
2 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iy}$
3 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iz}$
4 $\frac{\mu_{0}}{R} I \hat{x}$
5 $\frac{\mu_{0}}{R} \mathrm{Iy}$
Moving Charges & Magnetism

153437 A $50 \mathrm{~cm}$ long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?

1 $10.5 \mathrm{~A}$
2 $12.5 \mathrm{~A}$
3 $25.0 \mathrm{~A}$
4 $20.0 \mathrm{~A}$
Moving Charges & Magnetism

153438 Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\left|\frac{\mathrm{B}_{X}}{\mathrm{~B}_{\mathrm{Y}}}\right|$ is

1 $1: 4$
2 $2: 1$
3 $1: 2$
4 $4: 1$
Moving Charges & Magnetism

153439 A solenoid of length $2 \mathrm{~m}$ carries a current of 20A. The diameter of the solenoid is $3 \mathrm{~cm}$. If the magnetic field inside the solenoid is $20 \mathrm{mT}$, then the length of wire forming the solenoid is (assume, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

1 $100 \mathrm{~m}$
2 $125 \mathrm{~m}$
3 $175 \mathrm{~m}$
4 $150 \mathrm{~m}$
Moving Charges & Magnetism

153445 Consider a circular loop of radius $R$ on the $x-y$ plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by

1 $\frac{\mu_{0}}{2 R} I \hat{x}$
2 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iy}$
3 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iz}$
4 $\frac{\mu_{0}}{R} I \hat{x}$
5 $\frac{\mu_{0}}{R} \mathrm{Iy}$
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Moving Charges & Magnetism

153437 A $50 \mathrm{~cm}$ long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?

1 $10.5 \mathrm{~A}$
2 $12.5 \mathrm{~A}$
3 $25.0 \mathrm{~A}$
4 $20.0 \mathrm{~A}$
Moving Charges & Magnetism

153438 Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\left|\frac{\mathrm{B}_{X}}{\mathrm{~B}_{\mathrm{Y}}}\right|$ is

1 $1: 4$
2 $2: 1$
3 $1: 2$
4 $4: 1$
Moving Charges & Magnetism

153439 A solenoid of length $2 \mathrm{~m}$ carries a current of 20A. The diameter of the solenoid is $3 \mathrm{~cm}$. If the magnetic field inside the solenoid is $20 \mathrm{mT}$, then the length of wire forming the solenoid is (assume, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

1 $100 \mathrm{~m}$
2 $125 \mathrm{~m}$
3 $175 \mathrm{~m}$
4 $150 \mathrm{~m}$
Moving Charges & Magnetism

153445 Consider a circular loop of radius $R$ on the $x-y$ plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by

1 $\frac{\mu_{0}}{2 R} I \hat{x}$
2 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iy}$
3 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iz}$
4 $\frac{\mu_{0}}{R} I \hat{x}$
5 $\frac{\mu_{0}}{R} \mathrm{Iy}$
Moving Charges & Magnetism

153437 A $50 \mathrm{~cm}$ long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?

1 $10.5 \mathrm{~A}$
2 $12.5 \mathrm{~A}$
3 $25.0 \mathrm{~A}$
4 $20.0 \mathrm{~A}$
Moving Charges & Magnetism

153438 Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\left|\frac{\mathrm{B}_{X}}{\mathrm{~B}_{\mathrm{Y}}}\right|$ is

1 $1: 4$
2 $2: 1$
3 $1: 2$
4 $4: 1$
Moving Charges & Magnetism

153439 A solenoid of length $2 \mathrm{~m}$ carries a current of 20A. The diameter of the solenoid is $3 \mathrm{~cm}$. If the magnetic field inside the solenoid is $20 \mathrm{mT}$, then the length of wire forming the solenoid is (assume, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

1 $100 \mathrm{~m}$
2 $125 \mathrm{~m}$
3 $175 \mathrm{~m}$
4 $150 \mathrm{~m}$
Moving Charges & Magnetism

153445 Consider a circular loop of radius $R$ on the $x-y$ plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by

1 $\frac{\mu_{0}}{2 R} I \hat{x}$
2 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iy}$
3 $\frac{\mu_{0}}{2 \mathrm{R}} \mathrm{Iz}$
4 $\frac{\mu_{0}}{R} I \hat{x}$
5 $\frac{\mu_{0}}{R} \mathrm{Iy}$