Part (d) Enter an expression in Cartesian unit vector notation for a rotation, de, by an angle de about the positive z axis. Expression : de = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p Part (e) Enter an expression, in simplified form, for the amount of work, dW, done by the electric field on the dipole when it undergoes a rotation by d0. Expression : dW = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p Part (f) By performing an indefinite integral, determine the amount of work, W, required for a finite rotation by an angle 0. For your constant or integration use C. Expression : W = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), 4, 0, î, j, k, a, b, C, d0, E, m, p Part (g) Because the electric force is conservative, we re-express the work, W, done by the field in terms of potential energy, U. Recall that only changes in potential energy, AU, have physical meaning, so any constant term is arbitrary. Without loss of generality, set the constant C to zero, and enter an expression for the potential energy, U(0). Expression : U(0) = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p

Part (d) Enter an expression in Cartesian unit vector notation for a rotation, de, by an angle de about the positive z axis. Expression : de = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p Part (e) Enter an expression, in simplified form, for the amount of work, dW, done by the electric field on the dipole when it undergoes a rotation by d0. Expression : dW = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p Part (f) By performing an indefinite integral, determine the amount of work, W, required for a finite rotation by an angle 0. For your constant or integration use C. Expression : W = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), 4, 0, î, j, k, a, b, C, d0, E, m, p Part (g) Because the electric force is conservative, we re-express the work, W, done by the field in terms of potential energy, U. Recall that only changes in potential energy, AU, have physical meaning, so any constant term is arbitrary. Without loss of generality, set the constant C to zero, and enter an expression for the potential energy, U(0). Expression : U(0) = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), tan(0), q, 0, î, ĵ, k, a, b, C, d0, E, m, p