Field Due to a Solenoid

Q. Explain Why magnetic field outside the solenoid is zero?

Q.

What does the divergence of magnetic field lines near the ends of a current-carrying straight solenoid indicate?

Q. A coil is rotated with constant angular speed in a uniform magnetic field about an axis that is perpendicular to the field.

$\text{STATEMENT-1}:$ The EMF induced in the coil is maximum at the instant the magnetic flux through the coil is zero.

$\text{STATEMENT-2}:$ The angle between the normal to the coil and magnetic field induction is ${90}^{\circ }$.

1. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{TRUE}$ and $\text{STATEMENT-2}$ is the correct explanation of $\text{STATEMENT-1}$
2. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{TRUE}$ but $\text{STATEMENT-2}$ is the $\text{NOT}$ the correct explanation of $\text{STATEMENT-1}$
3. $\text{STATEMENT-1}$ is $\text{FALSE}$ and $\text{STATEMENT-2}$ is $\text{TRUE}$
4. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{WRONG}$

Q. A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy-$plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $\hat{n}$ direction. List–I gives time dependences of $\hat{n}$ in terms of a constant angular frequency $\omega$. List-II gives the torques experienced by the circular loop at time $t=\frac{\pi }{6\omega }\text{Let}\alpha =\frac{A^2{\mu }_0^2{m}^2{I}^2\omega }{2R}.$

	List-I		List-II
(I)	$\frac{1}{\sqrt{2}}(\sin \omega t\hat{j}+\cos \omega t\hat{k})$	(P)	$0$
(II)	$\frac{1}{\sqrt{2}}\left(\sin \omega t\widehat{i+\cos \omega t\hat{j}}\right)$	(Q)	$-\frac{\alpha }{4}\hat{i}$
(III)	$\frac{1}{\sqrt{2}}(\sin \omega t\hat{i}+\cos \omega t\hat{k})$	(R)	$\frac{3\alpha }{4}\hat{i}$
(IV)	$\frac{1}{\sqrt{2}}(\cos \omega t\hat{j}+\sin \omega t\hat{k})$	(S)	$\frac{\alpha }{4}\hat{j}$
		(T)	$-\frac{3\alpha }{4}\hat{i}$

Which one of the following options is correct

1. $I\to Q,II\to P,III\to S,IV\to R$
2. $I\to Q,II\to P,III\to S,IV\to T$
3. $I\to S,II\to T,III\to Q,IV\to P$
4. $I\to T,II\to Q,III\to P,IV\to R$

Q.

does magnetic field of solenoid depend upon radius?if it does why it is not included in the equation?

Q. Two cells of emf $E_1$ and $E_2(E_2>E_1)$ are connected in series in a secondary circuit of a potentiometer experiment for determination of emf. The balancing length is found to be 825 cm. Now when the terminals of cell of emf $E_1$ are reversed, then the balancing length is found to be 225 cm. The ratio of $E_1$ and $E_2$ is, then-

Q. Calculate the inductance of a solenoid containing 200 turns, a length of 25 cm and an area of cross section of $8c{m}^2$.

1. $2.4\times {10}^{-4}H$
2. $1.6\times {10}^{-4}H$
3. $3.2\times {10}^{-4}H$
4. $0.8\times {10}^{-4}H$

Q. In Fig. $\left(a\right)$ and Fig. $\left(b\right)$, two air-cored solenoids $P$ and $Q$ have been shown.

They are placed near each other. In Fig. $\left(a\right)$, when $I_P$ , the current in $P$, changes at the rate of $5\text{A/s}$, an emf of $2\text{mV}$ is induced in $Q$. The current in $P$ is then switched off, and a current changing at $2\text{A/s}$ is fed through $Q$ as shown in diagram. What emf will be induced in solenoid $P$?

1. $5\times {10}^{-3}\text{V}$
2. $8\times {10}^{-4}\text{V}$
3. $8\times {10}^{-2}\text{V}$
4. $2\times {10}^{-3}\text{V}$

Q.

A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10⁻⁴ m², carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.

(a) What is the magnetic moment associated with the solenoid?

(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10⁻² T is set up at an angle of 30º with the axis of the solenoid?

Q. Consider a metal ring kept on top of a fixed solenoid (say on a cardboard) (Figure). The center of the ring coincides with the axis of the solenoid. If the current is suddenly switched on, the metal ring jumps up. Explain

Q. The emf of a cell is $E\text{volt}$ and its internal resistance is $1\Omega$. A resistance of $4\Omega$ is joined to battery in parallel. This is connected in secondary circuit of potentiometer. The balancing length is $160\text{cm}$. If $1\text{V}$ cell balances for $100\text{cm}$ of potentiometer wire, then the emf of the cell is (Give integer value)

Q. Primary circuit of the potentiometer is shown in figure. Determine the potential gradient (means potential drop per unit length of potentiometer wire).

1. $\frac{20}{21}\text{V/m}$
2. $\frac{2}{21}\text{V/m}$
3. $\frac{5}{9}\text{V/m}$
4. $\frac{5}{8}\text{V/m}$

Q.

give two factors on which self inductance of a long solenoid depends.

Q. The magnetic induction inside a solenoid is $6.5\times {10}^{-4}$T. When it is filled with iron medium then the induction becomes 1.4 T. The relative permeability of iron will be

1. 2154
2. 2355
3. 1578
4. 1836

Q. The coefficient of self inductance of a solenoid is $0.18\text{mH}$. If a rod of soft iron, of relative permeability $900$, is inserted in it, the coefficient of self inductance will become -

1. $5.4\text{mH}$
2. $162\text{mH}$
3. $0.6\text{mH}$
4. $0.2\text{mH}$

Q. A circular coil of radius $2.5\text{cm}$ carries current of $2\text{A}$. If the coil has $50$ turns. Find the magnetic field at the center of the coil ? <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->

1. $\frac{\pi }{6250}\text{T}$
2. $\frac{\pi }{625}\text{T}$
3. $\frac{\pi }{125}\text{T}$
4. $\frac{\pi }{1250}\text{T}$

Q.

The current in a long solenoid of radius R and having n turns per unit length is given $i=i_0\sin \omega t.$ A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

Q. A magnetic flux of $8\times {10}^{-4}\text{Wb}$ is linked with each turn of a $200$ turns coil when there is an electric current of $4\text{A}$ in it. Calculate the self inductance of the coil.

1. $10\text{mH}$
2. $20\text{mH}$
3. $40\text{mH}$
4. $50\text{mH}$

Q. Is Magnetic field at one end of an infinite solenoid along the axis? If a is the area of cross section of solenoid with I current and n turns per unit length.then what is the flux of mf at the end of an infinite solenoid?

Q. For the shown arrangement of potentiometer, Find the value of $x$ , if $\text{P}$ is a null point. Resistance of portion $\text{OB}$ is $20\Omega$

1. $x=\frac{8}{5}\text{m}$
2. $x=\frac{1}{6}\text{m}$
3. $x=\frac{5}{8}\text{m}$
4. $x=\frac{9}{10}\text{m}$

Q.

A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

Q. A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field B at the centre of the solenoid if it carries a current of 5 A?

Q. A standard cell of emf $E_0=1.11\text{V}$ is balanced against $72\text{cm}$ length of a potentiometer. The same potentiometer is used to measure the potential difference across the standard resistance $R=120\Omega$. When the ammeter shows a current of $7.8\text{mA}$, a balanced length of $60\text{cm}$ is obtained on the potentiometer. Estimate the percentage error in the measurement of ammeter:

1. $1.3$
2. $2.5$
3. $0.5$
4. $2.75$

Q. A rod of length $l=0.5\text{m}$ is rotating with an angular speed $\omega =10\text{rad/s}$ about its one end which is at a distance $a=1\text{m}$ from an infinitely long wire carrying current $i=1\text{A}.$ Find the emf induced in the rod at the instant shown in the figure. Rod and wire both are lying in the same plane.

1. $0\text{V}$
2. $2\times {10}^{-6}[0.5-\ln (1.5\left)\right]\text{V}$
3. $4\times {10}^{-6}[1-\ln (2\left)\right]\text{V}$
4. $2\times {10}^{-6}[2-\ln (3\left)\right]\text{V}$

Q. Two moving coil meters, M1 and M2 have the following particulars:R1 = 10 W, N1 = 30, A1 = 3.6 × 10–3 m2, B1 = 0.25 TR2 = 14 W, N2 = 42, A2 = 1.8 × 10–3 m2, B2 = 0.50 T (The spring constants are identical for the two meters).Determine the ratio of (a) current sensitivity and (b) voltagesensitivity of M2 and M1.

Q. A moving coil galvanometer has following characteristics,
Number of turns = $80$, Area of coil =$50{\text{mm}}^2$, Resistance of coil = $20\Omega$, magnetic field = $0.2\text{T}$, torsional constant of the suspension wire = $5\times {10}^{-9}\text{N-m/rad}$.
Which of the following statements are correct.

1. Voltage sensitivity of the device is $8\text{div/mV}$
2. All of the above.
3. The angular deflection produced due to a potential difference of $0.01\text{mV}$ is $0.08\text{div}$
4. Current sensitivity of the device is $160\text{div/mA}$

Q.

A longer solenoid of diameter $0.1m$ has $2\times {10}^4$ turns per meter. At the center of the solenoid, a coil of $100$ turns and radius $0.01m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0A$ from $4A$ in $0.05s$. If the resistance of the coil is $10{\pi }^2\Omega$, the total charge flowing through the coil during this time is

1. $26\pi \mu C$
2. $32\mu C$
3. $16\pi \mu C$
4. $32\pi \mu C$

Q. A closely wound solenoid of 2000 turns and area of cross-section1.6 × 10–4 m2, carrying a current of 4.0 A, is suspended through itscentre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid? (b) What is the force and torque on the solenoid if a uniformhorizontal magnetic field of 7.5 × 10–2 T is set up at an angle of30° with the axis of the solenoid?

Q. A long solenoid of diameter $0.1m$ has $2\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius $0.01m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0A$ from $4A$ in $0.05s$. If the resistance of the coil is $10{\pi }^2\Omega$, the total charge flowing through the coil during this time is

1. $32\pi \mu C$
2. $64\pi \mu C$
3. $8\pi \mu C$
4. $16\pi \mu C$

Q. A constant current i is maintained in a solenoid. Which of the following quantities will increase if an iron rod is inserted in the solenoid along its axis?
(a) magnetic field at the centre
(b) magnetic flux linked with the solenoid
(c) self-inductance of the solenoid
(d) rate of Joule heating.