Lenz's Law

Q. The electric field at a distance $\frac{3R}{2}$ from the cente of a charged conducting spherical shell of radius $R$ is $E$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is

1. zero
2. $E$
3. $\frac{E}{2}$
   
4. $\frac{E}{3}$
   

Q. Consider a sphere of radius $R$, which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it, as shown, the ratio $\frac{\left|{\overrightarrow{E}}_A\right|}{\left|{\overrightarrow{E}}_B\right|}$ of the magnitudes of electric field $\overrightarrow{E_A}\text{and}\overrightarrow{E_B}$, respectively, at points $A$ and $B$, due to the remaining portions is:

1. $\frac{21}{34}$
2. $\frac{18}{34}$
3. $\frac{17}{54}$
4. $\frac{18}{54}$

Q.

An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true?

1. The electron path will be circular about the axis

2. The electron path will be accelerated along the path

3. The electron will continue to move with uniform velocity along the axis of the solenoid

4. The electron path will experience a force and will hence execute a helical path

Q.

What devices use AC and DC?

Q. In an $L-C$ oscillation circuit, maximum charge on capacitor can be $Q_0$. If at any instant the electrical energy is $\frac{3}{4}th$ of the magnetic energy, then the charge on the capacitor at that instant is

1. $\frac{2Q_0}{3}$
2. $\sqrt{\frac{3}{7}}{Q}_0$
3. $\frac{3}{7}{Q}_0$
4. $\sqrt{\frac{2}{3}}{Q}_0$

Q. An alternating voltage $v\left(t\right)=220\sin 100\pi tvolt$ is applied to a purely resistive load of $5\Omega$. The time taken for the current to rise from half of the peak value to the peak value is

1. $2.2ms$
2. $5ms$
3. $3.3ms$
4. $7.2ms$

Q.

Lenz’s law is a consequence of the law of conservation of

1. Charge

2. Mass

3. Energy

4. Momentum

Q. A positively charged sphere of radius $r_0$ carries a volume charge density $\rho$ as shown in figure. A spherical cavity of radius $\frac{r_0}{2}$ is then scooped out and left empty. $C_1$ is the centre of the sphere and $C_2$ is the centre of the cavity. What is the direction and magnitude of the electric field at point B?

1. $\frac{17\rho r_0}{54{ϵ}_0}$, towards left
2. $\frac{\rho r_0}{6{ϵ}_0}$, towardsleft
3. $\frac{17\rho r_0}{54{ϵ}_0}$, towards right
4. $\frac{\rho r_0}{6{ϵ}_0}$, towards right

Q. An electron moves along the line AB, which lies in the same plane as a circular loop of conducting wires as shown in the diagram. What will be the direction of current induced if any, in the loop

1. The current will be clockwise.
2. No current will be induced.
3. The current will be anticlockwise.
4. The current will change direction as the electron passes by.

Q.

If the number of turns of a solenoid is doubled keeping other factors constant, how does the self inductance of the soleniod change?

Q.

What is the function of a galvanometer in a circuit?

Q. The current through a coil of self inductance L = 2 mH is given by $I=t^2{e}^{–t}$ at time t. How long it will take to make the emf zero?

1. 2s
2. 3s
3. 1s
4. 4s

Q. A paramagnetic material has ${10}^{28}{\text{atoms/m}}^3$. Its magnetic susceptibility at temperature $350\text{K}$ is $2.8\times {10}^{-4}$. Its susceptibility at $300\text{K}$ is:

1. $3.726\times {10}^{-4}$
2. $3.672\times {10}^{-4}$
3. $2.672\times {10}^{-4}$
4. $3.267\times {10}^{-4}$

Q.

Consider a $72cm$ long wire $AB$ as shown in the figure. The galvanometer jockey is placed at $P$ on $AB$ at a distance $xcm$ from $A$. The galvanometer shows zero deflection. The value of $x$, to the nearest integer, is $\_\_\_\_\_\_$.

Q.

A long straight current-carrying wire passes normally through the center of the circular loop if the current through the wire increases. Will there be an induced emf in the loop? Justify?

Q.

What is a null point in a potentiometer?

Q. A $40\mu \text{F}$ capacitor in the defibrillator is charged to $3000\text{V}$. The energy stored in the capacitor is sent through a patient during a pulse of duration $2\text{ms}$. The power delivered to the patient is

1. $45\text{kW}$
2. $90\text{kW}$
3. $180\text{kW}$
4. $360\text{kW}$

Q.

A 50Hz AC current of crest value 1A flows through the primary coil of transformer. If mutual induction between primary and secondary is 1.5H, then the crest voltage induced in the secondary coil is:

1. 272V

2. 320V

3. 471V

4. 415V

Q. The current $‘i^{\prime }$ in an inductance coil varies with time $‘t^{\prime }$ according to the following graph


Which one of the following plots shows the variations of voltage in the coil magnitude wise? (all vertical lines are not part of graphs)

1. 
2. 
3. 
4. 

Q.

Why galvanometer is not used to measure current?

Q. The correct $I-H$ curve for paramagnetic materials is,

1. 
2. 
3. 
4. 

Q.

Two circular, similar, coaxial loops carry equal currents in the same direction. If the loops are brought nearer, what will happen?

Q. A spherical cavity of radius $R$ is cut from a non-conducting sphere of volulme charge density $\rho {\text{C/m}}^3$ as shown in figure. Find the magnitude of the net electric field at point $\text{P}$.

1. $\frac{\rho l}{3{\epsilon }_o}$
2. $\frac{3\rho l}{{\epsilon }_o}$
3. $\frac{\rho R}{2{\epsilon }_o}$
4. $\frac{\rho (r_1+r_2)}{3{\epsilon }_o}$

Q.

Does Lenzs law violate the law of conservation of energy? Justify your answer

Q.

A coil having n turns and resistance R ohm is connected with a galvanometer of resistance 4R ohm. This combination is moved in a region where magnetic flux changes from $W_{1}weberto{W}_2$ weber in t second. The induced current in the circuit is

1. $-\frac{n(W_2-W_1)}{5Rt}$

2. $-\frac{(W_2-W_1)}{Rnt}$

3. $-\frac{n(W_2-W_1)}{Rt}$

4. $-\frac{(W_2-W_1)}{5Rnt}$

Q. A uniform disc of radius a and mass m, is rotating freely with angular speed $\omega$ in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc and rotates with it. The new angular speed is

1. $\frac{\omega }{6}$
2. $\frac{\omega }{3}$
3. $\frac{\omega }{2}$
4. $\frac{\omega }{5}$

Q. A positive charge $q$ is placed in a spherical cavity made in a positively charged sphere. The centers of sphere and cavity are displaced by a small distance $\overrightarrow{l}$. Force on charge $q$ is:

1. In the direction parallel to vector $\overrightarrow{l}$
2. In radial direction
3. In the direction perpendicular to vector $\overrightarrow{l}$
4. Direction cannot be determined

Q. A bar magnet is moved in the direction indicated in the diagram between two coils PQ and CD. Predict the direction of induced current in each coil.

Q. A diamagnetic solution is poured into a
U-tube, and one arm of this U-tube is placed between the poles of strong magnet as shown in the diagram. The liquid level in the arm between the poles of strong magnet will -

1. rise
2. fall
3. remain as such
4. None of these

Q. A part of a circuit in steady state along with the current flowing in the branches, with value of each resistance is shown in figure. What will be the energy stored in the capacitor $C_0$

1. Zero
2. $6\times {10}^{-4}J$
3. $8\times {10}^{-4}J$
4. $16\times {10}^{-4}J$