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

153431 A long straight solenoid with cross sectional radius ' $a$ ' and number of turns per unit length ' $\mathrm{n}$ ' has a current varying width time as $\mathrm{I}\left(\mathrm{As}^{-1}\right)$. The magnitude of the electric field as a function of distance ' $r$ ' from the solenoid axis is

1 $\frac{n \mu_{0} \mathrm{a}^{2} \mathrm{I}}{2 \mathrm{r}}$
2 $\frac{\mu_{0} I n}{2 a}$
3 $\frac{\mathrm{na}^{2} \mathrm{I}}{2 \mu_{0} \mathrm{r}}$
4 $\frac{\mu_{0} \mathrm{Ia}}{2 \mathrm{n}}$
Moving Charges & Magnetism

153433 The magnetic field intensity $(\mathrm{H})$ at the centre of a long solenoid carrying a current of $2 \mathrm{~A}$, is found to be $1000 \mathrm{~A} / \mathrm{m}$. The number of turns per centimetre of the solenoid is
(Use $\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$ )

1 500
2 50
3 5
4 100
Moving Charges & Magnetism

153435 A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of 1000 turns. It carries a current of $10 \mathrm{~A}$. What is the magnitude of the magnetic field inside the solenoid?

1 $6.28 \times 10^{-3} \mathrm{~T}$
2 $2.51 \times 10^{-2} \mathrm{~T}$
3 $1.71 \times 10^{-2} \mathrm{~T}$
4 $7.23 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153436 Consider two solenoids $A$ and $B$ such that $L_{A}=$ $2 L_{B}$ and $A_{A}=\frac{1}{2} A_{B}$, Where $L_{A} \cdot A_{A}$ and $L_{B} \cdot A_{B}$ are the length and area of the two solenoids respectively. If the magnetic energy stored in the both solenoids is same. What should be the ratio of their magnetic fields $\frac{B_{A}}{B_{B}}=$

1 $1: 1$
2 $\sqrt{2}: 1$
3 $1: \sqrt{2}$
4 $1: 2$
Moving Charges & Magnetism

153431 A long straight solenoid with cross sectional radius ' $a$ ' and number of turns per unit length ' $\mathrm{n}$ ' has a current varying width time as $\mathrm{I}\left(\mathrm{As}^{-1}\right)$. The magnitude of the electric field as a function of distance ' $r$ ' from the solenoid axis is

1 $\frac{n \mu_{0} \mathrm{a}^{2} \mathrm{I}}{2 \mathrm{r}}$
2 $\frac{\mu_{0} I n}{2 a}$
3 $\frac{\mathrm{na}^{2} \mathrm{I}}{2 \mu_{0} \mathrm{r}}$
4 $\frac{\mu_{0} \mathrm{Ia}}{2 \mathrm{n}}$
Moving Charges & Magnetism

153433 The magnetic field intensity $(\mathrm{H})$ at the centre of a long solenoid carrying a current of $2 \mathrm{~A}$, is found to be $1000 \mathrm{~A} / \mathrm{m}$. The number of turns per centimetre of the solenoid is
(Use $\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$ )

1 500
2 50
3 5
4 100
Moving Charges & Magnetism

153435 A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of 1000 turns. It carries a current of $10 \mathrm{~A}$. What is the magnitude of the magnetic field inside the solenoid?

1 $6.28 \times 10^{-3} \mathrm{~T}$
2 $2.51 \times 10^{-2} \mathrm{~T}$
3 $1.71 \times 10^{-2} \mathrm{~T}$
4 $7.23 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153436 Consider two solenoids $A$ and $B$ such that $L_{A}=$ $2 L_{B}$ and $A_{A}=\frac{1}{2} A_{B}$, Where $L_{A} \cdot A_{A}$ and $L_{B} \cdot A_{B}$ are the length and area of the two solenoids respectively. If the magnetic energy stored in the both solenoids is same. What should be the ratio of their magnetic fields $\frac{B_{A}}{B_{B}}=$

1 $1: 1$
2 $\sqrt{2}: 1$
3 $1: \sqrt{2}$
4 $1: 2$
Moving Charges & Magnetism

153431 A long straight solenoid with cross sectional radius ' $a$ ' and number of turns per unit length ' $\mathrm{n}$ ' has a current varying width time as $\mathrm{I}\left(\mathrm{As}^{-1}\right)$. The magnitude of the electric field as a function of distance ' $r$ ' from the solenoid axis is

1 $\frac{n \mu_{0} \mathrm{a}^{2} \mathrm{I}}{2 \mathrm{r}}$
2 $\frac{\mu_{0} I n}{2 a}$
3 $\frac{\mathrm{na}^{2} \mathrm{I}}{2 \mu_{0} \mathrm{r}}$
4 $\frac{\mu_{0} \mathrm{Ia}}{2 \mathrm{n}}$
Moving Charges & Magnetism

153433 The magnetic field intensity $(\mathrm{H})$ at the centre of a long solenoid carrying a current of $2 \mathrm{~A}$, is found to be $1000 \mathrm{~A} / \mathrm{m}$. The number of turns per centimetre of the solenoid is
(Use $\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$ )

1 500
2 50
3 5
4 100
Moving Charges & Magnetism

153435 A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of 1000 turns. It carries a current of $10 \mathrm{~A}$. What is the magnitude of the magnetic field inside the solenoid?

1 $6.28 \times 10^{-3} \mathrm{~T}$
2 $2.51 \times 10^{-2} \mathrm{~T}$
3 $1.71 \times 10^{-2} \mathrm{~T}$
4 $7.23 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153436 Consider two solenoids $A$ and $B$ such that $L_{A}=$ $2 L_{B}$ and $A_{A}=\frac{1}{2} A_{B}$, Where $L_{A} \cdot A_{A}$ and $L_{B} \cdot A_{B}$ are the length and area of the two solenoids respectively. If the magnetic energy stored in the both solenoids is same. What should be the ratio of their magnetic fields $\frac{B_{A}}{B_{B}}=$

1 $1: 1$
2 $\sqrt{2}: 1$
3 $1: \sqrt{2}$
4 $1: 2$
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Moving Charges & Magnetism

153431 A long straight solenoid with cross sectional radius ' $a$ ' and number of turns per unit length ' $\mathrm{n}$ ' has a current varying width time as $\mathrm{I}\left(\mathrm{As}^{-1}\right)$. The magnitude of the electric field as a function of distance ' $r$ ' from the solenoid axis is

1 $\frac{n \mu_{0} \mathrm{a}^{2} \mathrm{I}}{2 \mathrm{r}}$
2 $\frac{\mu_{0} I n}{2 a}$
3 $\frac{\mathrm{na}^{2} \mathrm{I}}{2 \mu_{0} \mathrm{r}}$
4 $\frac{\mu_{0} \mathrm{Ia}}{2 \mathrm{n}}$
Moving Charges & Magnetism

153433 The magnetic field intensity $(\mathrm{H})$ at the centre of a long solenoid carrying a current of $2 \mathrm{~A}$, is found to be $1000 \mathrm{~A} / \mathrm{m}$. The number of turns per centimetre of the solenoid is
(Use $\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$ )

1 500
2 50
3 5
4 100
Moving Charges & Magnetism

153435 A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of 1000 turns. It carries a current of $10 \mathrm{~A}$. What is the magnitude of the magnetic field inside the solenoid?

1 $6.28 \times 10^{-3} \mathrm{~T}$
2 $2.51 \times 10^{-2} \mathrm{~T}$
3 $1.71 \times 10^{-2} \mathrm{~T}$
4 $7.23 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153436 Consider two solenoids $A$ and $B$ such that $L_{A}=$ $2 L_{B}$ and $A_{A}=\frac{1}{2} A_{B}$, Where $L_{A} \cdot A_{A}$ and $L_{B} \cdot A_{B}$ are the length and area of the two solenoids respectively. If the magnetic energy stored in the both solenoids is same. What should be the ratio of their magnetic fields $\frac{B_{A}}{B_{B}}=$

1 $1: 1$
2 $\sqrt{2}: 1$
3 $1: \sqrt{2}$
4 $1: 2$