Ncert Solutions Physics Class 12th

1.34 Suppose that the particle in Exercise in 1.33 is an electron projected with velocity  = 2.0 × 10⁶ m s^–1. If E between the plates separated by 0.5 cm is 9.1 × 10² N/C, where will the electron strike the upper plate? (|e|=1.6 × 10^–19 C, m_e = 9.1 × 10^–31 kg.)

1.32 (a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

1.31 It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

1.30 Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss’s law.

[Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

1.29  A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is ($\frac{\mathit{\sigma }}{2{\mathit{\epsilon }}_0}$  )  , where $\widehat{\mathit{n}}$ is the unit vector in the outward normal direction, and $\mathit{\sigma }\mathit{}$ is the surface charge density near the hole.

1.28 (a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.

(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. 1.36(b)].

(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

1.27 In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of   ${10}^5$ N${\mathit{C}}^{-1}$per meter. What are the force and torque experienced by a system having a total dipole moment equal to${10}^{-7}$  Cm in the negative z-direction?

1.26 Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?

1.25 An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 $\times {10}^4\mathit{}\mathit{N}{\mathit{C}}^{-1}$ (Millikan’s oil drop experiment). The density of the oil is 1.26 g /${\mathit{c}\mathit{m}}^3$  . Estimate the radius of the drop.

(g = 9.81 m/${\mathit{s}}^2$ ; e = 1.60 $\times {10}^{-19}$ C).

1.24 Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0  $\times {10}^{-22}\mathit{}$ C/${\mathit{m}}^2$. What is E:

(a) In the outer region of the first plate

(b) In the outer region of the second plate

(c) Between the plates?