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question_answer1) A metal ring of radius\[r=0.5m\]with its plane normal to a uniform magnetic field B of induction 0.2 T carries a current\[I=100A\]. The tension (in newtons) developed in the ring is-
question_answer2) A wire bent in the form of a right angled triangle ABC as shown in fig. carries a current 1A. It is placed in the region of a unifrom magnetic induction field \[B=0.2T\]as shown in fig. If\[AC=1m\]. the net force (in N) on the wire is-
question_answer3) A copper wire having resistance 0.01 ohm in each metre is used to wind a 400 turn solenoid of radius 1.0 cm and length 20 cm. The emf (in V) of a battery which when connected across the solenoid will cause a magnetic field of \[1.0\times {{10}^{-2}}\]T near the centre of the solenoid-
question_answer4) A particle having a charge of\[20\mu C\]and mass \[20\mu g\]moves along a circle of radius\[5.0cm\]under the action of a magnetic field\[B=1.0\text{ }T\]. Now a uniform electric field is switched on and it is found that the particle continues on the tangent with a uniform velocity. The electric field (in V/m) will be-
question_answer5) The magnetic field at two points on the axis of a circular coil at distances of 0.05m and 0.2m from the centre are in the ratio 8:1. The radius (in m) of the coil is ?
question_answer6) The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is\[54\mu T\]. What will be its value (in \[\mu T\]) at the centre of the loop-
question_answer7) A non-relativistic proton beam passes without deviation through the region of space where there are uniform transverse mutually perpendicular electric and magnetic fields with\[E=120\text{ }kV/m\]and\[B=50mT\]. Then the beam strikes a grounded target. Find the force (in\[\mu N\]) with which the beam acts on the target if the beam current is equal to\[I=0.80mA.\]
question_answer8) Two metal strips, each of length 2m, are clamped parallel to each other on a horizontal floor with a separation 1m between them. A wire of mass m lies on them perpendicularly as shown in figure. A vertically upward magnetic field of strength B exists in the space. The metal strips are smooth but the coefficient of friction between the wire and the floor is\[\mu \]. A current i is established when the switch S is closed at the instant\[t=0\]. How far (in meter) away from the strips will the wire reach? (assume \[i=\]constant) \[(i=2amp.=0.2,\text{ }m=1kg,\text{ }B=1T)\]
question_answer9) A circular loop of radius r carrying a current i is held at the centre of another circular loop of radius\[R(>>r)\]carrying a current I. The plane of the smaller loop makes an angle of \[30{}^\circ \]with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of this force? If it is\[\frac{{{\mu }_{0}}\pi iIr}{aR}\]. Find a.
question_answer10) Electric charge q is uniformly distributed over a rod of length ℓ. The rod is placed parallel to a long wire carrying a current i. The separation between the rod and the wire is a. Find the force needed to move the rod along its length with a uniform velocity v. If it is\[\frac{{{\mu }_{0}}i}{\pi }\times xN\]. Find x. \[(q=2C,\text{ }V=2m/s,\text{ }a=1m)\]
question_answer11) A square cardboard of side ℓ and mass m is suspended from a horizontal axis XY as shown in figure. A single wire is would along the periphery of board and carrying a clockwise current I. At\[t=0\], a vertical downward magnetic field of induction B is switched on. Find the minimum value of B (in T) so that the board will be able to rotate up to horizontal level. (\[m=1kg,\text{ }I1\]amp, \[\ell =1\]metre)
question_answer12) A U-shaped wire of mass m and length\[\ell \] is immersed with its two ends in mercury (see figure). The wire is in a homogeneous field of magnetic induction B. If a charge, that is, a current pulse\[q=\int{i\,dt}\], is sent through the wire, the wire will jump up. Calculate, the height h (in metre) that the wire reaches, assuming that the time of the current pulse is very small in comparison with the time of flight. \[\left( \frac{q}{m}=2C/kg,\ell =1m,B=5T \right)\].
question_answer13) There exists a uniform and electric field of magnitude 1T and 1V/m respectively along positive y-axis. A charged particle of mass 1 kg and charge 1 C moving with velocity 1 m/sec along x-axis is at origin at\[t=0\]. If the coordinates of particle at time \[\pi \]seconds is given as (X, Y, Z) in meter, then find the value of \[\left( XY+YZ+ZX \right)\times \frac{5}{{{\pi }^{2}}}\].
question_answer14) A uniform wooden bar of mass \[\frac{\pi }{100}\]kg and radius kg and radius of cross-section 10 cm carries a light coil C of 100 turns. The bar is smoothly pivoted at P. If the coil carries a current 2A and subjected to external magnetic field\[{{10}^{-2}}T\], the bar remains in equilibrium, the distance x (in cm) of the C.M. of the rod from the pivot is\[10\times a\], then the value of a is.
question_answer15) An infinite uniform current carrying wire is kept along z-axis, carrying current \[{{I}_{0}}\]in the direction of the positive z-axis.\[OABCDEFG\]represents a circle (where all the points are equally spaced), whose centre at point (4m, 0m) and radius 4 m a shown in the figure. If \[\int\limits_{DEF}{{\vec{B}}}.d\vec{\ell }=\frac{{{\mu }_{0}}{{I}_{0}}}{K}\]in S.I. units, then find the value of k.
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A current i is established when the switch S is closed at the instant\[t=0\]. How far (in meter) away from the strips will the wire reach? (assume \[i=\]constant) \[(i=2amp.=0.2,\text{ }m=1kg,\text{ }B=1T)\] 
Calculate, the height h (in metre) that the wire reaches, assuming that the time of the current pulse is very small in comparison with the time of flight. \[\left( \frac{q}{m}=2C/kg,\ell =1m,B=5T \right)\]. 
