A current carrying closed loop in the form of a right angle isosceles triangle ABC is placed in uniform magnetic field acting along AB. If the magnetic force on the arm BC is $$\overrightarrow {F,} $$ the force on the arm AC is

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 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 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