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A long solenoid of radius $R$ carries a time (t)-dependent current $I(t)=I_{0}t(1−t)$. A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0≤t≤1$, the induced current $(I_{R})$ and the induced $EMF(V_{R})$ in the ring change as:

A conducting circular loop made of a thin wire, has area $3.5×10_{−3}m_{2}$ and resistance $10Ω$. It is placed perpendicular to a time dependent magnetic field $B(t)=(0.4T)sin(50πt)$. The field is uniform in space. Then the net charge flowing through the loop during $t=0s$ and $t=10ms$ is close to:

The figure shows a square loop $L$ of side $5cm$ which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1cms_{−1}$. At some instant, a part of L is in a uniform magnetic field of $1T$, perpendicular to the plane of the loop. If the resistance of $L$ is $1.7Ω$, the current in the loop at that instant will be close to :

A power transmission line feeds input power at $2300V$ to a step down transformer with its primary windings having $4000$ turns, giving the output power at $230V$. If the current in the primary of the transformer is $5A$, and its efficiency is $90%$, the output current would be:

A coil of cross-sectional area $A$ having $n$ turns is placed in a uniform magnetic field $B$. When it is rotated with an angular velocity $ω$, the maximum e.m.f. induced in the coil will be

A small circle loop of wire of radius a is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I+I_{o}cos(ωt)$ . The emf induced in the smaller inner loop is nearly :

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $_{′}v_{′}$ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $σ_{1}$ and $σ_{2}$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is $240ms_{−1}$. The earth's magnetic field over Delhi is $5×10_{−5}$ T with the declination angle $∼0_{o}$ and dip of $θ$ such that $sinθ=32 $. If the voltage developed is $V_{B}$ between the lower and upper side of the plane and $V_{W}$ between the tips of the wings then $V_{B}$ and $V_{W}$ are close to

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as $B=B_{0}e_{−t/τ}$, where $B_{0}$ and $τ$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time $(t→∞)$ is