A rectangular coil of n turns each of area A, carrying current I, when suspended in a uniform magnetic field B, experiences a torque
\(\tau =nI \ BA \ sin\theta \)
Where is \(\theta \) the angle which a normal drawn on the plane of coil makes with the direction of magnetic field. This torque tends to rotate the coil and bring it in an equilibrium position. In the stable equilibrium state, the resultant force on the coil is zero. The torque on the coil is also zero and the coil has minimum potential energy.
Read the above passage and answer the following questions:
(i) In which position, a current carrying coil suspended in uniform magnetic field experiences
(a) minimum torque and
(b) maximum torque?
(ii) a circular coil of 200 turns, radius 5 cm carries a current of 2.0 A. It is suspended vertically in a uniform horizontal magnetic field of 0.20 T, with the plane of the coil making an angle with \(60°\) the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning.
(iii) what is the basic value displayed by the above study?

A physics teacher tells his students in the class that in paramagnetic materials, every atom has some permanent magnetic dipole moment. In the absence of an external magnetic field, the atomic dipoles are randomly oriented so that average magnetic moment per unit volume of the material behaves as a magnet. When an external magnetic field is applied, the torque developed tries to align the atomic magnetic dipoles in the direction of the field. That is why the specimen gets magnetized weekly in the direction of the field.
Read the above passage and answer the following questions:
(i) Name any three paramagnetic materials
(ii) Name any two ferromagnetic materials. How is their behavior different from that of paramagnetic materials?
(iii) The teacher asks the students how true is the famous saying: 'Spare the rod and spoil the child', comment.

Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density \(\sigma\) .
(ii) An infinitely large thin plane sheet has a uniform surface charge density \(+\sigma\). Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet.

An electric dipole of dipole moment p consists of point charges +q and q separated by a distance 2a apart. Deduce the expression for the electric field E due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment p. Hence, show that in the limit
x >> a, E \(\longrightarrow\) 2P\((4\pi{\epsilon}_{0}{x}^{3})\).
Given the electric field in the region E = 2x \(\hat{i}\), find the net electric flux through the cube and the charge enclosed by it.

(i) If two similar large plates, each of area A having surface charge densities +σ and -σ are separated by a distanced in air, find the expression for
(a) field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.
(b) the potential difference between the plates.
(c) the capacitance of the capacitor so formed.
(ii) Two metallic spheres of radii R and 2R are charged, so that both of these have same surface charge density σ.  If they are connected to each other with a conducting wire, in which direction will the charge flow and why?

Two capacitors \(3\mu F\) and \(6\mu F\) are connected in series with a 6V battery. A cross which of the capacitors will there be larger potential difference?

A regular hexagon of side 10 cm has a charge 5\(\mu\) C at each of its vertices. Calculate the potential at the centre of the hexagon.

Two point charge of \(+3\times {{10}^{-8}}C\) and \(-2\times {{10}^{-8}}C\) are located 15cm apart in air. Find at what point on the joining these charge the electric potential is zero. Take potential at infinity to be zero.

Four point charge 10^-8 C,\(−2×{{10}^{−8}}C\) and \(-4\times {{10}^{-8}}C\) and \(6\times {{10}^{-8}}C\) are placed at the four corners of a square of side \(2\sqrt { 2 }cm. \) Calculate the electric potential at the centre of square.

Calculate the potential at the centre of a square of side \(\sqrt { 2 } m\), which carries at its four corners charges of +2nC, +1nC, -2nC and -3nC respectively.