A circular coil of radius 6 cm and 20 turns rotates about its vertical diameter with an angular speed of 40 rad $s^{-1}$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2}$ T. If the coil form a closed loop of resistance 8 $\Omega$, then the average power loss

The axle of a circular wheel of radius R is held horizontally by two identical strings of equal lengths separated by a distance D. The tension in each string is $T _0$. The rim of the wheel carries a total charge $+$Q distributed uniformly on it. The wheel is vertical and is kept in a uniform vertical magnetic field $\vec{B}$. It is now rotated at an angular speed $\omega$. If the string break at a tension of $3T _0/2$, than the maximum possible value of $\omega$ at which the wheel can be rotated without breaking a string is $\dfrac{DT _0}{QBR^2}$.

A conductor of $3\ m$ length is moving perpendicular to its length as well as a magnetic field of ${10}^{-3}\ T$ with a speed of ${10}\ m/s$, then the force required to move it with this constant speed is

A horizontal straight conductor (otherwise placed in a closed circuit) along east-west direction falls under gravity. There is:-

In a uniform magnetic field of induction $B$ a wire in the form of semicircle of radius $r$ rotated about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$ the mean power generated per period of rotation is:

To produce a field of magnetic $\pi$ tesla at the center of circular loop of diameter 1 m, the current flowing through loop is :

A metal ring of radius $r = 0.5\ m$ with its plane normal to a uniform magnetic field $B$ of induction $0.2\ T$ carries a current $I = 100\ A$. The tension in newtons developed in the ring is

A magnet is brought towards a coil (i) speedly (ii) slowly, then the induced electromotive force charge will be respectively

An electric charge $+ q$ moves with velocity $\bar{V}=3\hat{i}+4\hat{j}+\hat{k}$, in an electromagnetic field given by $\bar{E}=3\hat{i}+\hat{j}+\hat2{k}$ $\bar{B}=\hat{i}+\hat{j}+\hat3{k}$.The y-component of the force experienced by +q is:

A boat is moving due East in region where the earth's magnetic field is $5.0 \times {10^{ - 5}}\,N{A^{ - 1}}{m^{ - 1}}$ North and horizontal. The boat carries a vertical aerial $2 m$ long. if the speed of the boat is $1.50\,ms - 1,$ the magnitude of the induced emf in the wire of aerial is 

 A coil of circular cross-section having $100$ turns and $4 \mathrm { cm } ^ { 2 }$ face area is placed with its axis parallel to a magnetic field which decreases by $10 ^ { - 2 } \mathrm { Wb } \mathrm { m } ^ { - 2 }$ in $0.01 \mathrm { s }$. The e.m.f induced in the coil is: 

Radius of current carrying coil is 'R'. The ratio of magnetic field at a axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil :-

The magnetic induction due to a magnet on the equatorial line at a distance 0.2 m is $54 \times 10^{-6}$T. The magnetic induction at 0.3m is

A uniform metal rod is moving with a uniform velocity $v$ parallel to a long straight wire carrying a current $I$. The rod is perpendicular to the wire with its ends at distances $r _{1}$ and $r _{2}$ with $(r _{2} > r _{1})$ from it. The emf induced in the rod is

If the permeability of iron piece is $3 \times 10 ^ { - 3 }$ and intensity of magnetising field of iron piece is 120 A/m, then what is the magnetic induction of iron piece 

A conducting ring of radius r is placed perpendicularly inside a time verying magnetic field given by $B={ B } _{ 0 }+\alpha t.{ B } _{ 0 }$ and $\alpha $ are positive constants. E. m. f induced in the ring is 

In the figure magnetic points into the plane of paper and the rod of length $l$ is moving in the field such that the bottom most point has a velocity $v _1$ and the topmost point has the velocity $V _2(V _2>V _1)$ The emf induced is given by 

A uniform magnetic field exists in region given by $\vec B = 3\hat i + 4\hat j + 5\hat k$. A rod of length $5m$ is placed along $y$ moved along $x-axis$ with constant speed $1m/sec$. Then induced e.m.f. in the rod will be:

A square coil of side 0.5$\mathrm { m }$ has movable side It is placed such that its plane is perpendicularuniform magnetic field of induction 0.2$\mathrm { T }$ . If all sides are allowed to move with a speed of 0.1for 4 sec outwards, average indaced emf is

The amplitude of a magnetic field, which is part of a harmonic electromagnetic wave in vacuum, is  $\mathrm { B } _ { 0 } =510\mathrm { nT } .$  What is the amplitude of the electric field of the wave? 

A  $1\mathrm { m }$  long conducting rod rotates with an angular frequency of  $400\mathrm { rad } \mathrm { s } ^ { - 1 }$  about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant magnetic field of  $0.5\mathrm { T }$  parallel to the axis exists everywhere.Calculate the e.m.f developed between the center and the ring?

A charged particle enters in a uniform magnetic field with velocity at an angle of ${ 60 }^{ o }$ with the magnetic field. The pitch of helical path is x, the radius of helix is 

When a charged particle is projected perpendicular to a magnetic field then the

A $0.1m$ long conductor carrying a current of $50A$ is perpendicular to a magnetic field of $1.21mT$. The mechanical power to move the conductor with a speed of $1m{s}^{-1}$ is

A non conducting ring having charge q uniformly distributed over its circumference is placed on a rough horizontal surface. A vertical time varying magnetic field $B=4t^2$ is switched on a time $t=0$. Mass of the ring is m and radius is R. The ring starts rotating after $2$ seconds. The coefficient of friction between the ring and the tablets.