Moving Charges and Magnetism

A hollow, right circular cone of base radius R and height h, with its tip at the origin is rotating about the Z-axis with an angular velocity , as shown in the figure. The cone carries a total charge Q uniformly distributed on its curved surface. The magnitude of magnetic field at a point (0, 0, z), where z R and z h, is n 04 QR2 z3. The value of n is: [figure]

In a vacuum chamber, a particle of charge 1 and mass 1 mg is projected with a velocity ( i+2 j) m s-1 from the XZ plane at time t=0 in an electric field of 1 i V m-1. At t=0.2 s, the electric field is switched off and a magnetic field of 6 j T is switched on. The acceleration due to gravity is -10 j m s-2. Correct option(s) is/are:

1. The vertical distance of the particle from the XZ plane at t=0.3 s is 15 cm.
2. The vertical distance of the particle from the XZ plane at t=0.4 s is 10 cm.
3. The radius of the trajectory of the particle for t>0.2 s is 20 cm.
4. The particle will be in the XZ plane at t=0.35 s.

A conducting solid sphere of radius R and mass M carries a charge Q. The sphere is rotating about an axis passing through its center with a uniform angular speed . The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as Q2M. The value of is

An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field B. The magnitude of the line integral B dl along a straight line from the point (- 3a, a, 0) to (a, a, 0) is given by [ 0 is the magnetic permeability of free space.]

1. 7 0 I/24
2. 7 0 I/12
3. 0 I/8
4. 0 I/6

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass m and radius r and it is in a uniform vertical magnetic field B0, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity g, on two conducting supports at P and Q. When a current I is passed through the loop, the loop turns about the line PQ by an angle given by [figure]

1. = rIB0/(mg)
2. = 2 rIB0/(mg)
3. = rIB0/(2mg)
4. = mg/( rIB0)

A positive, singly ionized atom of mass number AM is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width w with magnetic field B0 = 0.1 k Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory. [Given: Mass of neutron/proton = (5/3) 10-27 kg, charge of the electron = 1.6 10-19 C.] [figure] Which of the following option(s) is(are) correct?

1. The value of x for H+ ion is 4 cm.
2. The value of x for an ion with AM = 144 is 48 cm.
3. For detecting ions with 1 AM 196, the minimum height (x1 - x0) of the detector is 55 cm.
4. The minimum width w of the region of the magnetic field for detecting ions with AM = 196 is 56 cm.