A length - scale `(l)` depends on the permittivity `(epsilon)` of a dielctric material. Boltzmann constant `(k_(B))`, the absolute tempreture `(T)`, the number per unit volume `(n)` of certain charged particles, and the charge `(q)` carried by each of the partcles. which of the following expression `(s)` for `I` is `(are)` dimensionally correct?

A length -scale (l) depends on the permittivity (epsilon) of a dielectric material, Boltzmann constant (k_(B)) , the absolute temperature (T), the number pr unit volume (n) of certain charged paticles, and the charge (q) carried by each of the particles. Which of the following expression for l is dimensionally correct?

A conductor of length of l and area of cross section A has n number of electrons per unit volume of the conductor. The total charge carried by the conductor is

A particle of charge q and mass m enters normally (at point P) in a region of magnetic field with speed v. It comes out noramally from Q after time T as shown in Fig. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression (s) is are correct?

A particle of charge q and mass m enters normally (at point P) in a region of magnetic field with speed v. It comes out noramally from Q after time T as shown in Fig. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression (s) is are correct?

The current in a copper wire is increased by increasing the potential difference between its end. Which one of the following statements regarding n, the number of charge carriers per unit volume in the wire and v the drift velocity of the charge carriers is correct -

There is a fixed sphere of radius R having positive charge Q uniformly spread in its volume. A small particle having mass m and negative charge (– q) moves with speed V when it is far away from the sphere. The impact parameter (i.e., distance between the centre of the sphere and line of initial velocity of the particle) is b. As the particle passes by the sphere, its path gets deflected due to electrostatics interaction with the sphere. (a) Assuming that the charge on the particle does not cause any effect on distribution of charge on the sphere, calculate the minimum impact parameter b0 that allows the particle to miss the sphere. Write the value of b_(0) in term of R for the case 1/2mV^(2)=100.((kQq)/(R)) (b) Now assume that the positively charged sphere moves with speed V through a space which is filled with small particles of mass m and charge – q. The small particles are at rest and their number density is n [i.e., number of particles per unit volume of space is n]. The particles hit the sphere and stick to it. Calculate the rate at which the sphere starts losing its positive charge (dQ)/(dt). Express your answer in terms of b_(0)