Field Due to a Solenoid

Q.

A long solenoid of diameter 0.1m has 2×10⁴ turns per meter. At the center of the solenoid, a coil of 100 turns and a radius of 0.01 m 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 10π²Ω the total charge flowing through the coil during this time is?

1. 32 πμC

2. 32 μC

3. 16 πC

4. 16 πμ

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

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

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.

An ideal solenoid of cross-sectional area ${10}^{-4}{m}^2$ has 500 turns per metre. At the centre of this solenoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 millisecond, the emf developed in the second coil is

1. 1 mV

2. 2 mV

3. 3 mV

4. 4 mV

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. $2.75$
3. $2.5$
4. $0.5$