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A conducting loop of radius R is present in a uniform magnetic field B perpendicular to the plane of the ring. If radius R varies as a function of time 't', as $\mathrm{R} = {\mathrm{R}}_0 + \mathrm{t}.$ The e.m.f induced in the loop is
                                                  
1.  $2\mathrm{\pi }\left({\mathrm{R}}_0 + \mathrm{t}\right) \mathrm{B} \mathrm{clockwise}$
2.  $\mathrm{\pi }\left({\mathrm{R}}_0 + \mathrm{t}\right) \mathrm{B} \mathrm{clockwise}$
3.  $2\mathrm{\pi }\left({\mathrm{R}}_0 + \mathrm{t}\right) \mathrm{B} \mathrm{anticlockwise}$
4.  $\mathrm{Zero}$
 

An electron is moving in a circular orbit of radius R with an angular acceleration $\alpha$. At the centre of the orbit is kept a conducting loop of radius r, (r < < R). The e.m.f induced in the smaller loop due to the motion of the electron is-
1.  $\mathrm{Zero}, \mathrm{since} \mathrm{charge} \mathrm{on} \mathrm{electron} \mathrm{in} \mathrm{constant}$
$$
2.  $\frac{{\mathrm{\mu }}_0{\mathrm{er}}^2}{4\mathrm{R}}\mathrm{\alpha }$
3.  $\frac{{\mathrm{\mu }}_0{\mathrm{er}}^2}{4\mathrm{\pi R}}\mathrm{\alpha }$
4.  $\mathrm{None} \mathrm{of} \mathrm{these}$
 

A square coil ABCD is placed in the x-y plane with its center at the origin. A long straight wire, passing through carries a current in the negative z-direction. Current in this wire increases with time. The induced current in the coil is
                                                  
1.  Clockwise
2.  Anticlockwise 
3.  Zero
4.  Alternating

Consider the situation shown in fig. The resistance less wire AB is slide on the fixed rails with a constant velocity. If the wire AB is replaced by a resistance less semicircular wire, the magnitude of the induced current will
                                                       
1.  Increase
2.  Remain the same
3.  Decrease
4.  Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it

A semicircular conducting wire is placed in yz plane in a uniform magnetic field directed along positive z-direction. An induced emf will be developed between the ends of the wire if it is moved along. 
                                                              
1.  Positive x-direction
2.  Positive y-direction
3.  Positive z-direction
4.  None of these

A square loop of side a and resistance R is moved in the region of uniform magnetic field B (loop remaining completely inside field), with a velocity v through a distance x. The work done is
1.  $\frac{{\mathrm{Bl}}^2\mathrm{vx}}{\mathrm{R}}$
2.  $\frac{\mathit{2}{\mathit{B}}^{\mathit{2}}{\mathit{l}}^{\mathit{2}}\mathit{v}\mathit{x}}{\mathit{R}}$
3.  $\frac{4{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{vx}}{\mathrm{R}}$
4.  None of these

A copper rod AB of length L, pivoted at one end A, rotates at a constant angular velocity $\omega$, at right angles to a uniform magnetic field of induction B. The e.m.f developed between the midpoint C of the rod and end B is
                                                            
1.  $\frac{B\omega l^2}{4}$
2.  $\frac{B\omega l^2}{2}$
3.  $\frac{3B\omega l^2}{4}$
4.  $\frac{3B\omega l^2}{8}$
 

$\mathrm{In} \mathrm{this} \mathrm{circuit} \mathrm{shown}, \mathrm{X} \mathrm{is} \mathrm{joined} \mathrm{to} \mathrm{Y} \mathrm{for} \mathrm{a} \mathrm{long} \mathrm{time}, \mathrm{and} \mathrm{then} \mathrm{x} \mathrm{is}$
$\mathrm{joined} \mathrm{to} \mathrm{Z}. \mathrm{The} \mathrm{total} \mathrm{heat} \mathrm{produced} \mathrm{in} R_2 \mathrm{is}:$
                                                     
1.  $\frac{{\mathrm{LE}}^2}{2{\mathrm{R}}_1^2}$
2.  $\frac{{\mathrm{LE}}^2}{2{\mathrm{R}}_2^2}$
3.  $\frac{{\mathrm{LE}}^2}{2{\mathrm{R}}_1{\mathrm{R}}_2}$
4.  $\frac{{\mathrm{LE}}^2{\mathrm{R}}_2}{2{\mathrm{R}}_1^2}$
 

$\mathrm{Two} \mathrm{inductors} {\mathrm{L}}_1 \mathrm{and} {\mathrm{L}}_2 \mathrm{are} \mathrm{connected} \mathrm{in} \mathrm{parallel} \mathrm{and} \mathrm{a} \mathrm{time} \mathrm{varying} \mathrm{current} \mathrm{i} \mathrm{flows} \mathrm{as} \mathrm{shown}.$
$\mathrm{The} \mathrm{ratio} \mathrm{of} \mathrm{currents} {\mathrm{i}}_1/{\mathrm{i}}_2 \mathrm{at} \mathrm{any} \mathrm{time} \mathrm{t} \mathrm{is}$
1.  ${\mathrm{L}}_1/{\mathrm{L}}_2$
2.  ${\mathrm{L}}_2/{\mathrm{L}}_1$
3.  $\frac{{\mathrm{L}}_1^2}{{\left({\mathrm{L}}_1 + {\mathrm{L}}_2\right)}^2}$
4.  $\frac{{\mathrm{L}}_2^2}{{\left({\mathrm{L}}_1 + {\mathrm{L}}_2\right)}^2}$

A flexible circular loop 20 cm in diameter lies in a magnetic field with magnitude 1.0 T, directed into the plane of the page as shown in the figure. The loop is pulled at the points indicated by the arrows, forming a loop of zero areas in 0.314 s.
                                              
The average induced emf in the circuit is
1.  0.2 V
2.  0.1 V
3.  1 V
4.  10 V 
 

A circular loop of radius R carrying current I lies in the x-y plane with its center at the origin. The total magnetic flux through the x-y plane is 
(1) Directly proportional to I
(2) Directly proportional to R
(3) Directly proportional to R²
(4) Zero

The figure shows two parallel and coaxial loops. The smaller loop (radius r) is above the larger loop (radius R), by distance x >> R. The magnetic field due to current I in the larger loop is nearly Constant throughout the smaller loop. Suppose that x is increasing at a constant rate of dx/dt = v.
                                                                       
Determine the magnetic flux through the smaller loop as a function of x.
1.  $\frac{{\mu }_{0}i{R}^2\pi r^2}{x^3}$
2.  $\frac{{\mu }_{0}i{R}^2\pi r^2}{2x^3}$
3.  $\frac{2{\mu }_{0}i{R}^2\pi r^2}{x^3}$
4.  $\frac{\sqrt{2}{\mu }_{0}i{R}^2\pi r^2}{x^3}$
 
 

The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is 10Ω. The current in the circuit will be now

(1) i = 0.5 A
(2) i > 0.5 A
(3) i < 0.5 A
(4) i = 0

A brilliant student of physics developed a magnetic balance to weigh objects. The mass m to be measured is hung from the center of the bar. The bar is kept in a uniform magnetic field of 1.5 T directed into the plane of the figure. Battery voltage can be adjusted to vary the current in the circuit. The horizontal bar shown in 60 cm long and is made of extremely lightweight material. It is connected to the battery via a resistance. There is no tension in the supporting-wires. The magnetic force only supports the hanging weight.
                                                                  
Which point of the battery terminal is positive?
1.  A 
2.  B
3.  Either A and B
4. Cannot be found
 

A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width d in its circumference. The solenoid has a cross-sectional area A and a uniform internal field of magnitude B₀. Now beginning at t = 0, the solenoid current is steadily increased so that the field magnitude at any time t is given by B(t) = B₀ + αt where α > 0. Assuming that no charge can flow across the gap, the end of the ring which has an excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively

(1) X, Aα
(2) X πR²α
(3) Y, πA²α
(4) Y, πR²α

A long solenoid of N turns has a self-inductance L and area of cross-section A. When a current I flows through the solenoid, the magnetic field inside it has magnitude B. The current i is equal to:
1.  BAN/L
2.  BANL
3.  BN/AL
4.  B/ANL
 
 

In the circuit shown in the figure, switch S is closed at t = 0 Then
                                                     
1.  After a long time, interval potential difference across the capacitor and inductor will be equal
2.  After a long time interval charge on the capacitor will E C.
3.  After a long time interval current in the inductor will be E/R.
4.  After a long time interval current through battery will be same as the current through it  initially

Two coils of self-inductance 100 mH and 400 mH are placed very close to each other. Find the maximum mutual inductance between the two when 4A current passes through them.
1.  200 mH
2.  300 mH
3.  $100\sqrt{2}\mathrm{mH}$
4. None of these