A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field B$${\mathop i\limits^ \wedge }$$ . The torque on the coil due to the magnetic field is :

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms^–2, what will be the tensile stress that would be developed in the wire ?

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He⁺ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is :

Ship A is sailing towards north-east with velocity $$\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge $$ km/hr where $$\mathop i\limits^ \wedge $$ points east and $$\mathop j\limits^ \wedge $$ , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in :