A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is $$i$$. The resultant magnetic field due to the two semicircular parts at their common centre is

A closely wound solenoid of 2000 turns and area of cross-section 1.5 $$ \times $$ 10^$$-$$4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 $$ \times $$ 10^$$-$$2 tesla making an angle of 30^o with the axis of the solenoid. The torque on the solenoid will be

A particle having a mass of 10^$$-$$2 kg carries a charge of 5 $$ \times $$ 10^$$-$$8 C. The particle is given an initial horizontal velocity of 10⁵ m s^$$-$$1 in the presence of electric field $$\overrightarrow E $$ and magnetic field $$\overrightarrow B $$. To keep the particle moving in a horizontal direction, it is necessary that
(1)  $$\overrightarrow B $$ should be perpendicular to the direction of velocity and $$\overrightarrow E $$ should be along the direction of velocity

(2)  Both $$\overrightarrow B $$ and $$\overrightarrow E $$ should be along the direction of velocity

(3)  Both $$\overrightarrow B $$ and $$\overrightarrow E $$ are mutually perpendicular and perpendicular to the direction of velocity.

(4)  $$\overrightarrow B $$ should be along the direction of velocity and $$\overrightarrow E $$ should be perpendicular to the direction of velocity

Which one of the following pairs of statements is possible ?

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is the net force on the remaining three arms of the loop is