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

153456 A toroid has a non-ferromagnetic core of inner radius $20.5 \mathrm{~cm}$ and outer radius $21.5 \mathrm{~cm}$, around which 4200 turns of a wire are wound. If the current in the wire is $10 \mathrm{~A}$, the magnetic field inside the core of the toroid is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathbf{H m}^{-1}\right)$

1 $20 \mathrm{mT}$
2 $40 \mathrm{mT}$
3 $20 \pi \mathrm{mT}$
4 $40 \pi \mathrm{mT}$
Moving Charges & Magnetism

153457 A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per unit length is tripled and the current is halved, then the new value of the magnetic field will be

1 $4 \mathrm{~B}$
2 $2 \mathrm{~B}$
3 $\frac{3 \mathrm{~B}}{2}$
4 $\frac{\mathrm{B}}{2}$
Moving Charges & Magnetism

153458 Two long parallel wires carry equal current $i$ flowing in the same direction are at a distance 2d apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and at a distance $x$ from the midpoint is -

1 $\frac{\mu_{0} i d}{\pi\left(d^{2}+x^{2}\right)}$
2 $\frac{\mu_{0} i x}{\pi\left(d^{2}-x^{2}\right)}$
3 $\frac{\mu_{0} i x}{\left(d^{2}+x^{2}\right)}$
4 $\frac{\mu_{0} \text { id }}{\left(d^{2}+x^{2}\right)}$
Moving Charges & Magnetism

153459 A straight conductor of length $32 \mathrm{~cm}$ carries a current of $30 \mathrm{~A}$. Magnetic induction at a point in air at a perpendicular distance of $12 \mathrm{~cm}$ from the mid-point of the conductor is

1 $0.2 \mathrm{G}$
2 $0.3 \mathrm{G}$
3 $0.4 \mathrm{G}$
4 $0.5 \mathrm{G}$
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Moving Charges & Magnetism

153456 A toroid has a non-ferromagnetic core of inner radius $20.5 \mathrm{~cm}$ and outer radius $21.5 \mathrm{~cm}$, around which 4200 turns of a wire are wound. If the current in the wire is $10 \mathrm{~A}$, the magnetic field inside the core of the toroid is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathbf{H m}^{-1}\right)$

1 $20 \mathrm{mT}$
2 $40 \mathrm{mT}$
3 $20 \pi \mathrm{mT}$
4 $40 \pi \mathrm{mT}$
Moving Charges & Magnetism

153457 A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per unit length is tripled and the current is halved, then the new value of the magnetic field will be

1 $4 \mathrm{~B}$
2 $2 \mathrm{~B}$
3 $\frac{3 \mathrm{~B}}{2}$
4 $\frac{\mathrm{B}}{2}$
Moving Charges & Magnetism

153458 Two long parallel wires carry equal current $i$ flowing in the same direction are at a distance 2d apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and at a distance $x$ from the midpoint is -

1 $\frac{\mu_{0} i d}{\pi\left(d^{2}+x^{2}\right)}$
2 $\frac{\mu_{0} i x}{\pi\left(d^{2}-x^{2}\right)}$
3 $\frac{\mu_{0} i x}{\left(d^{2}+x^{2}\right)}$
4 $\frac{\mu_{0} \text { id }}{\left(d^{2}+x^{2}\right)}$
Moving Charges & Magnetism

153459 A straight conductor of length $32 \mathrm{~cm}$ carries a current of $30 \mathrm{~A}$. Magnetic induction at a point in air at a perpendicular distance of $12 \mathrm{~cm}$ from the mid-point of the conductor is

1 $0.2 \mathrm{G}$
2 $0.3 \mathrm{G}$
3 $0.4 \mathrm{G}$
4 $0.5 \mathrm{G}$
Moving Charges & Magnetism

153456 A toroid has a non-ferromagnetic core of inner radius $20.5 \mathrm{~cm}$ and outer radius $21.5 \mathrm{~cm}$, around which 4200 turns of a wire are wound. If the current in the wire is $10 \mathrm{~A}$, the magnetic field inside the core of the toroid is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathbf{H m}^{-1}\right)$

1 $20 \mathrm{mT}$
2 $40 \mathrm{mT}$
3 $20 \pi \mathrm{mT}$
4 $40 \pi \mathrm{mT}$
Moving Charges & Magnetism

153457 A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per unit length is tripled and the current is halved, then the new value of the magnetic field will be

1 $4 \mathrm{~B}$
2 $2 \mathrm{~B}$
3 $\frac{3 \mathrm{~B}}{2}$
4 $\frac{\mathrm{B}}{2}$
Moving Charges & Magnetism

153458 Two long parallel wires carry equal current $i$ flowing in the same direction are at a distance 2d apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and at a distance $x$ from the midpoint is -

1 $\frac{\mu_{0} i d}{\pi\left(d^{2}+x^{2}\right)}$
2 $\frac{\mu_{0} i x}{\pi\left(d^{2}-x^{2}\right)}$
3 $\frac{\mu_{0} i x}{\left(d^{2}+x^{2}\right)}$
4 $\frac{\mu_{0} \text { id }}{\left(d^{2}+x^{2}\right)}$
Moving Charges & Magnetism

153459 A straight conductor of length $32 \mathrm{~cm}$ carries a current of $30 \mathrm{~A}$. Magnetic induction at a point in air at a perpendicular distance of $12 \mathrm{~cm}$ from the mid-point of the conductor is

1 $0.2 \mathrm{G}$
2 $0.3 \mathrm{G}$
3 $0.4 \mathrm{G}$
4 $0.5 \mathrm{G}$
Moving Charges & Magnetism

153456 A toroid has a non-ferromagnetic core of inner radius $20.5 \mathrm{~cm}$ and outer radius $21.5 \mathrm{~cm}$, around which 4200 turns of a wire are wound. If the current in the wire is $10 \mathrm{~A}$, the magnetic field inside the core of the toroid is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathbf{H m}^{-1}\right)$

1 $20 \mathrm{mT}$
2 $40 \mathrm{mT}$
3 $20 \pi \mathrm{mT}$
4 $40 \pi \mathrm{mT}$
Moving Charges & Magnetism

153457 A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per unit length is tripled and the current is halved, then the new value of the magnetic field will be

1 $4 \mathrm{~B}$
2 $2 \mathrm{~B}$
3 $\frac{3 \mathrm{~B}}{2}$
4 $\frac{\mathrm{B}}{2}$
Moving Charges & Magnetism

153458 Two long parallel wires carry equal current $i$ flowing in the same direction are at a distance 2d apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and at a distance $x$ from the midpoint is -

1 $\frac{\mu_{0} i d}{\pi\left(d^{2}+x^{2}\right)}$
2 $\frac{\mu_{0} i x}{\pi\left(d^{2}-x^{2}\right)}$
3 $\frac{\mu_{0} i x}{\left(d^{2}+x^{2}\right)}$
4 $\frac{\mu_{0} \text { id }}{\left(d^{2}+x^{2}\right)}$
Moving Charges & Magnetism

153459 A straight conductor of length $32 \mathrm{~cm}$ carries a current of $30 \mathrm{~A}$. Magnetic induction at a point in air at a perpendicular distance of $12 \mathrm{~cm}$ from the mid-point of the conductor is

1 $0.2 \mathrm{G}$
2 $0.3 \mathrm{G}$
3 $0.4 \mathrm{G}$
4 $0.5 \mathrm{G}$