Concider the situation shown in figure .The width of each plate is b.The capacitor plates are rigidly clamped in the laboratory and connected to be a battery of emf `epsilon` All surfaces are frictionless .Calculate the value of`M` for which the dielectric slab will stay in equilibrium.

In the situation shown in figure, both the pulleys and the strings are light and all the surfaces are frictionless. The acceleration of mass M, tension in the string PQ and force exerted by the clamp on the pulley, will respectively be -

Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A. (a) Calculate the capacitance and the rate of change of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Two metallic plate A and B , each of area 5 xx 10^(-4)m^(2) , are placed parallel to each at a separation of 1 cm plate B carries a positive charge of 33.7 xx 10^(-12) C A monocharonatic beam of light , with photoes of energy 5 eV each , starts falling on plate A at t = 0 so that 10^(16) photons fall on it per square meter per second. Assume that one photoelectron is emitted for every 10^(6) incident photons fall on it per square meter per second. Also assume that all the emitted photoelectrons are collected by plate B and the work function of plate A remain constant at the value 2 eV Determine (a) the number of photoelectrons emitted up to i = 10s, (b) the magnitude of the electron field between the plate A and B at i = 10 s, and (c ) the kinetic energy of the most energotic photoelectrons emitted at i = 10 s whenit reaches plate B Negilect the time taken by the photoelectrons to reach plate B Take epsilon_(0) = 8.85 xx 10^(-12)C^(2)N- m^(2)

Two blocks each of mass m, connected by an un-stretched spring are kept at rest on a frictionless horizontal surface. A constant force F is applied on one of the blocks pulling it away from the other as shown in figure. (a)Find accelaration of the mass center. (b) Find the displacement of the centre of mass as function of time t. (c) If the extension of the spring is X_(0) at an instant t, find the displacements of the two blocks relative to the ground at this instant.

In the circuit diagram given in figure suppose the resistors R_1, R_2 and R_3 have the values 5Omega, 10 Omega, 30 Omega respectively, which have been connected to a battery of 12V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance.

A parallel plate air capacitor of capacitance C is connected to a cell o f emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d_(1) and dielectric constant k_(1) and the other has thickness d_(2) and dielectric constant k_(2) as shown in figure. This arrangement can be thought as a dielectric slab of thickness d = ( d_(1) + d_(2) ) and effective dielectric constant k. The k is ...... (a) (K_(1)d_(1)+K_(2)d_(2))/(d_(1)+d_(2)) (b) (K_(1)d_(1)+K_(2)d_(2))/(K_(1)+K_(2)) (c) (K_(1)K_(2)(d_(1)+d_(2)))/((K_(1)d_(2)+K_(2)d_(1))) (d) (2K_(1)K_(2))/(K_(1)+K_(2))