Equations e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 are approximations of the magnitude of the electric field of an electric dipole, at points along the dipole axis. consider a point p on that axis at distance z = 8.00d from the dipole center (where d is the separation distance between the particles of the dipole). let eappr be the magnitude of the field at point p as approximated by e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 (electric dipole). let eact be the actual magnitude. by how much is the ratio eappr/eact less than 1?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final

The total amount of energy contained in an object