Moving Charges and Magnetism · Question 3

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.