Show that the vector field F= 2x(y2+z3)I +2x2yj + 3x2z2k

The magnetic field inside a superconducting solenoid is 4.50 t. the solenoid has an inner diameter of 6.20 cm and a length of 26.0 cm. determine (a) the magnetic energy density in the field and (b) the energy stored in the magnetic field within the solenoid.

Aparticle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 8.00î m/s. find (a) the vector position of the particle at any time t (where t is measured in seconds), (b) the velocity of the particle at any time t, (c) the position of the particle at t = 7.00 s, and (d) the speed of the particle at t = 7.00

Asatellite that goes around the earth once every 24 hours iscalled a geosynchronous satellite. if a geosynchronoussatellite is in an equatorial orbit, its position appearsstationary with respect to a ground station, and it is known as ageostationary satellite find the radius rof the orbit of a geosynchronous satellite that circles the earth.(note that ris measured from the center of the earth, not the surface.) you mayuse the following constants: the universal gravitational constant g is 6.67 \times 10^{-11}\; {\rm n \; m^2 / kg^2}. the mass of the earth is 5.98 \times 10^{24}\; {\rm kg}. the radius of the earth is 6.38 \times 10^{6}\; {\rm m}.