A square loop $MNOP$ of side $20 \mathrm{cm}$ is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the Fig. 6.75. The loop is pulled with a constant velocity of $20 \mathrm{cm} {\mathrm{s}}^{-1}$ till it goes out of the field.

(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?

(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.

A square loop of side $20 \mathrm{cm}$ is initially kept $30 \mathrm{cm}$ away from a region of uniform magnetic field of $0.1 \mathrm{T}$ as shown in Fig. 6.77. It is then moved towards the right with a velocity of $10 \mathrm{cm} {\mathrm{s}}^{-1}$ till it goes out of the field. Plot a graph showing the variation of magnetic flux ($\varphi$) through the loop with time ($t$).

A square loop of side $20 \mathrm{cm}$ is initially kept $30 \mathrm{cm}$ away from a region of uniform magnetic field of $0.1 \mathrm{T}$ as shown in Fig. 6.77. It is then moved towards the right with a velocity of $10 \mathrm{cm} {\mathrm{s}}^{-1}$ till it goes out of the field. Plot a graph showing the variation of induced emf ($\epsilon$) in the loop with time $t$.

A square loop of side $20 \mathrm{cm}$ is initially kept $30 \mathrm{cm}$ away from a region of uniform magnetic field of $0.1 \mathrm{T}$ as shown in Fig. 6.77. It is then moved towards the right with a velocity of $10 \mathrm{cm} {\mathrm{s}}^{-1}$ till it goes out of the field. Plot a graph showing the variation of induced current in the loop if it has resistance of $0.1 \mathrm{\Omega }$.

Figure 6.79 shows a rectangular conducting loop $PQSR$ in which arm $RS$ of length '$l$' is movable. The loop is kept in a uniform magnetic field '$B$' directed downward perpendicular to the plane of the loop. The arm $RS$ is moved with a uniform speed '$v$'.

Deduce the expression for the emf induced across the arm '$RS$'.

Figure 6.79 shows a rectangular conducting loop $PQSR$ in which arm $RS$ of length '$l$' is movable. The loop is kept in a uniform magnetic field '$B$' directed downward perpendicular to the plane of the loop. The arm $RS$ is moved with a uniform speed '$v$'.

Deduce the expression for the external force required to move the arm.

Figure 6.79 shows a rectangular conducting loop $PQSR$ in which arm $RS$ of length '$l$' is movable. The loop is kept in a uniform magnetic field '$B$' directed downward perpendicular to the plane of the loop. The arm $RS$ is moved with a uniform speed '$v$'.

Deduce the expression for the power dissipated as heat.

A rectangular conductor, $LMNO$, is placed in a uniform magnetic field $\overrightarrow{B}$, directed perpendicular to the plane of the conductor (as shown in Fig. 6.80). Obtain an expression, for the emf induced in the arm $MN$, when the arm is moved towards the left with a speed $v$.