An infinitely long thin wire carrying a uniform linear static charge density `lambda` is place along the z-axis (Fig. Ep 8.28). The wire is set into motion along its length with a uniform velocity `vecv=v hatk_z`. Calculate the poynting vector `vecS=1/mu_0(vecExxvecB)`.

A thin straight infinitely long conducting wire having charge density lambda is enclosed by a cylindrical surface of radius r and lengh l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

A non-conducting disc of radius a and uniform positive surface charge density sigma is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disc, from a height H with zero initial velocity. The particle has q//m=4 in_0 g//sigma Find the value of H if the particle just reaches the disc.

A straight segment OC(of length L meter) of a circuit carrying a current I amp is placed along the x- axis ( fig.). Two infinitely long straight wires A and B , each extending from z = -oo to +oo , are fixed at y = -a meter and y = +a meter respectively, as shown in the figure. If the wires A and B each carry a current I amp into the plane of the paper, obtain the expression for the force acting on the segment OC. What will be the force on OC if the current in the wire B is reversed?

A copper rod of length 0.18 m is moving with a uniform velocity 10 ms^-1 parallel to a long straight wire carrying a current of 5.0 A. The rod itself is perpendicular to the wire with its ends at distances 0.01 m and 0.2 m from it. Calculate the e.m.f. induced in the rod.

Two long wires carrying current I_1 and I_2 are arranged as shown in figure. The one carrying current I_1 is along the x-axis. The other carrying current I_2 is along a line parallel to the y-axis given by x=0 and z=d. Find the force exerted at O_2 because of the wire along the x-axis.

A circular ring of radius R with uniform positive charge density lambda per unit length is located in the y z plane with its center at the origin O. A particle of mass m and positive charge q is projected from that point p( - sqrt(3) R, 0,0) on the negative x - axis directly toward O, with initial speed V. Find the smallest (nonzero) value of the speed such that the particle does not return to P ?

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field vec(B) = (3 hat(i) + 4hat(k)) B_(0) exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium What is the direction of the current I in PQ?

A right circular cylinder of length L (in m) and of radius R (in m) has its center at the origin and its length along the X-axis. A uniform electric field vecE = E_x hat I N C^-1 for x > 0 and vec E = -E_xhati NC^-1 for x < 0 exists over the cylinder. Find the net charge enclosed by the cylinder.

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . The current in the coil in (a) is switched off and the coil s positioned as shown in the figure. The coil is then turned thorugh an angle of 90^@ in a time of 0.14 s. Calculate the average e.m.f. induced in the coil.

A uniform copper wire of mass 2.23xx10^(-3) kg carries a current of 1 A when 1.7 V is applied across it. Calculate its length and area of cross-section. If the wire is uniformly stretched to double its length, calculate the new resistance. Density of copper is 8.92xx10^(3) kg m^(-3) and resistivity is 1.7xx10^(-8) Omega m.