1.34) Suppose that the particle in is an electron projected with velocity . If E between the plates separated by 0.5 cm is , where will the electron strike the upper plate? (|e|=)
Q 1.33: A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx .The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is .
Q 1.32(b): Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.
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.
1.31 It is now believed 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 + e, and the ‘down’ quark (denoted by d) of charge 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.
Q 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.]
Q 1.29: A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is , where is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.
1.28 (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
We know that electric field inside a conductor is zero.
Therefore, a possible way to shield from the strong electrostatic fields in its environment is to enclose the instrument fully by a metallic surface.
1.28 (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
Q 1.28 (a) A conductor A with a cavity as shown in Figure a is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.
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 per metre. What are the force and torque experienced by a system having a total dipole moment equal to Cm in the negative z-direction ?
Q 1.25: An oil drop of 12 excess electrons is held stationary under a constant electric field of (Millikan’s oil drop experiment). The density of the oil is 1.26 g cm-3. Estimate the radius of the drop.