Two circular loops are placed with their centres separted by a fixed distance. How would you orient the loops to have (a) the largest mutual inductance (b) the smallest mutual inducatance?

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L gt gt l ) . The loops are coplanar and their centres coincide. Find the mutual inductance of the system.

A circular loop is prepared from a wire of uniform cross section. A battery is connected between any two points on its circumference. The magnetic induction at the centre of the loop is ______ .

Two concentric circular coils, one of small radius r_1 and the other of large radius r_2 , such that r_1 lt lt r_2 , are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in figure. (b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s. Calculate the induced emf in the loop at the instant when x = 0.2 m. Take a = 0.1 m and assume that the loop has a large resistance.

Two beads of masses m_(1) and m_(2) are closed threaded on a smooth circular loop of wire of radius R. Intially both the beads are in position A and B in vertical plane . Now , the bead A is pushed slightly so that it slide on the wire and collides with B . if B rises to the height of the centre , the centre of the loop O on the wire and becomes stationary after the collision , prove m_(1) : m_(2) = 1 : sqrt(2)

Two circular loops A and B of radii R and 2R respectively are made of the similar wire. Their moments of inertia about the axis passing through the centre of perpendicular to their plane are I_(A)" and "I_(B) respectively. The ratio (I_(A))/(I_(B)) is :

(a) A closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets ? (b) A closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. (c) A rectangular loop and a circular loop are moving out of a uniform magnetic field region (Figure) to a field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops.

A straight wire carrying a current of 12 A is bent into a semicircular arc of radius 2.0 cm as shown in figure (a). Consider the magnetic field vecB at the centre of the arc. (a) What is the magnetic field due to the straight segments ? (b) In what way the contribution to vecB from the semicircle differs from that of a circular loop and in what way does it resemble ? ( c) Would your answer be different if the wire were bent into a semicircular arc of the same radius but in the opposite way as shown in figure (b) ?