A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 A distributed uniformly across its cross...

1. A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the same direction. What is the magnitude of the magnetic field 3.0 mm from the axis?2. A loop of wire (resistance = 2.0 m) is positioned as shown with respect to a long wire which carries a current. If d = 1.0 cm, D = 6.0 cm, and L = 1.5 m, what current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s?3. A deuteron is accelerated from rest through a 10-kV potential difference and then moves perpendicularly to a uniform magnetic field with B = 1.6 T. What is the radius of the resulting circular path? (deuteron: m = 3.3 x 10^-27 kg, q = 1.6 x 10^-19 C)4. A particle (mass = 2.0 mg, charge = –6.0 µC) moves in the positive direction along the x axis with a velocity of 3.0 km/s. It enters a magnetic field of (2.0i + 3.0j + 4.0k) mT. What is the acceleration of the particle?