Using Lenz's Law

Q. Consider two parallel, conducting frictionless tracks are kept in gravity free space as shown in the figure. A movable conductor $PQ$, initially kept at $OA$, given a velocity $10{\text{ms}}^{-1}$ towards right. If space contains a magnetic field upon the distance moved by conductor $PQ$ from $OA$ line and given by $\overrightarrow{B}=cx(-\hat{k})$$[c=\text{constant}=1$$\text{S.I. unit}]$. The mass of conductor $PQ$ is $1\text{kg}$ and length of $PQ$ is $1\text{m}$. Answer the following questions based on above passage.

1. The distance travelled by conductor when its speed is $5{\text{ms}}^{-1}$ is ${\left(\frac{10}{2}\right)}^{\frac{1}{3}}\text{m}$
2. The heat loss during the time interval $t=0$ to time $t$ sec, when the speed of conductor is $5{\text{ms}}^{-1}$ is $50\text{J}$
3. The distance travelled by conductor when its speed is $5{\text{ms}}^{-1}$ is${\left(\frac{15}{2}\right)}^{\frac{1}{3}}\text{m}$
4. The heat loss during the time interval $t=0$ to time $t$ sec, when the speed of conductor is $5{\text{ms}}^{-1}$ is $10\text{J}$

Q. The magnetic flux linked with a coil at any instant ‘t’ is given by $\varphi =5t^3-100t+300,$ the e.m.f. induced in the coil at t = 2 second is

1. 40 V
2. 140 V
3. – 40 V
4. 300 V

Q. A coil having an area $A_0$ is placed in a magnetic field. The field intensity changes from $B_0$ to $4B_0$ in time interval of ‘t’. The magnitude of emf induced in the coil will be _____.

1. $\frac{A_0{B}_0}{t}$
2. $\frac{3A_0{B}_0}{t}$
3. $\frac{3B_0}{A_{0}t}$
4. $\frac{4B_0}{A_{0}t}$

Q. Magnetic flux passing through a coil changes with time as, $\varphi =10t^2+5t+1$ where $\varphi$ is in m wb and t in sec. then magnitude of emf at t = 5s is

1. 0.105 V
2. 0.01V
3. 0.205V
4. 1.2 V

Q. A current carrying solenoid is approaching a conducting loop as shown in the figure. The direction of induced current as observed by an observer on the other side of the loop will be

1. Anticlockwise
2. Clockwise
3. East
4. West

Q. As shown in the figure, P and Q are two coaxial conducting loops separated by some distance. When the switch S is closed, a clockwise current $I_p$ flows in P (as seen by E) and an induced current $I_{Q1}$ flows in Q. The switch remains closed for a long time. When S is opened, a current $I_{Q2}$ flows in Q. Then the directions of $I_{Q1}$ and $I_{Q2}$ (as seen by E) are

1. Respectively anticlockwise and clockwise
2. Respectively clockwise and anticlockwise
3. Both clockwise
4. Both anticlockwise

Q. An electric potential difference will be induced between the ends of the conductor shown in the diagram, when the conductor moves in the direction

1. P
2. Q
3. M
4. L

Q. A circular coil of $20c{m}^2$ area is made of 100 turns as shown is figure. In 0.2 sec of time, $\overrightarrow{B}$ reverses its direction of the field. How much charge flows through wire, if R = 6 $\Omega$?

1. 0.16 C
2. 0.32 C
3. 0.28 C
4. 0.64 C

Q. A loop (circuit) is placed in uniform $\overrightarrow{B}$ & flux through the loop is given by $\varphi =4t$. Find the power supplied to the 6 volt battery.

1. 6 Watt
2. 2 Watt
3. 3 Watt
4. 5 Watt

Q. BAR magnet is moving along the axis of a loop & towards it as shown in the figure.

1. $V_A-V_B$ is negative
2. $V_A-V_B$ is positive
3. $V_A-V_B$ is zero
4. No current in the loop