Test: EMT - Magnetostatics

A long hollow coaxial wire lias inner radius a and outer radius b. Uniform current I flows along its inner surface and return through the outer surface as shown in figure. The magnitude vector potential in different regions are

A conducting wire carrying current I₀ is bent in the shape of a loop, as shown in figure. The magnetic field at Unseen point O is given by

A vector potntial at a point is given by  The current density corresponding to the vector potential is

Three infinitely-long conductors carrying currents I₁, I₂, and I₃ lie perpendicular to the plane of the paper as shown below. If the value of integral for the loops C₁, C₂, and C₃ are 2μ₀, 4_μ0 and μ₀ in the units of N/A, respectively, then

If a point dipole of the dipole moment is kept in external magnetic field  The force acting on the dipole is given by 

Consider two infinitely Ions wires parallel to the z-axis passing through the point and One is carrying current I₀ along positive z-direction of other one is carrying current 3I₀, along negative z-direetion. The value of  on closed curve (x - 1)² + y² = 16 along clockwise direction is _____ μ₀I₀.
(Answer should be integer).

An election is revolving around the nucleus in circular orbit of radius a₀ in a hydrogen atom. If electron is revolving with speed v₀ , the magnetic field at nucleus due to orbital motion of electron is . (Round off to two decimal places)

Two infintely long current carrying wire are placed along x and y axis and crossing through the origin as shown in figure. The magnetic field at (2, 3,4) will be

Two large parallel plates move with a constant speed v in the positive y direction as shown in figure. If both the plates have surface charge density σ, the magnetic force per unit area on the lower plate is

All infinitely long wire carrying current I₀ is placed (crossing through the origin) along x-axis and another wire of length L carrying current I₀ is placed mx-y plane, as shown in figure below. Thex-component of magnetic force acting on the wire is given by

The regions of space z < 0 and z > 0 are filled with free space and material having permeability 2_μ0 respectively. The magnetic field m the region  and the magnitude of magnetic field in region z > 0 is 6T. The angle between magnetic field and normal to the mterface in region z < 0 is given by

Two magnetic dipoles of magnitude m, one is placed at origin and the otherone is displaced from P to Q keeping the direction fixed (Assume that P and Q both are in x-y plane). The required work done to displaced the magnetic dipole from P to Q is

A ring of radius R carries a linear charge density λ. It is rotating about an axis crossing through its centre and perpendicular to its plane with an angular speed ω. The magnetic field on its axis at a distance  from the centre is ________ μ₀λω. (Round off to two decimal places)

A rigid square loop ABCD of side L is situated at a distance L from an infinite straight wire, with the side AB parallel to the infinite wire, as shown in the figure below. The infinite wire, which is in the plane of the loop, carries a current I from right to left. The value of  through the square loop is _____________ (Round off to two decimal places)

The volume current density through a long cylindrical conductor is given to be  where, R is radius of cylinder and r is tlie distance of some point from tlie axis of cylinder and J₀ is a constant. The value of r at which magnetic field maximum is ___________________ R. (Round off to two decimal places)

A long hollow cylinder of radius R carrying uniform surface charge density σ. It is rotating about its axis with angular speed ω. A ring of radius (r = R/2) is placed eo-axially with cylinder. The value of ton the ring is    ______ πμ₀ωσR³ (Round off to two decimal places)

A long solid conducting cylinder of radius R carrying volume current along its axis. The magnetic field inside the cylinder is given by (where J₀ is a constant and r is the distance from the it axis). The magnetic field at a distance r = 2R from it axis is______ 
(Upto two decimal places)