Magnetic Fields and Magnetic Circuits - Electricity and Magnetism - Instrumentation Engineering Previous Year Questions

A wire of circular cross section with radius a is shown in the figure. The current density is given by J = ks², where k is a constant, s is the radial distance from the axis and 0 ≤ s ≤ a. The total current I in the wire is

The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along the y direction. The coefficient of friction between the bar and the surface is 0.1. Assume the acceleration due to gravity to be 10 m/s². The system faces a uniform flux density B = -1 ẑ T. At time t = 0, a current of 10 A is switched onto the bar and is maintained.
When the bar has moved by 1 m, its speed in metre per second is ______ (rounded off to one decimal place).

A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. \(\mu_0 = 4\pi \times 10^{-7}\) H/m and \(\mu_R\) of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is ___.

The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 \(\mu\)N/m. When the gap is doubled, the force per unit length will be ______ \(\mu\)N/m (rounded off to one decimal place).

A straight thin wire carrying a current of I = 1 A in the direction
n = (1/√6)i + (2/√6)j + (1/√6)k is placed inside a magnetic field of B = (2i + 2k) T.
The force per unit length on the wire is ____ N/m.