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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

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can you please ans (d), (e), (f), (g)? 

Part (d) Enter an expression in Cartesian unit vector notation for a rotation, d0, 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), 9, 0, î, j, 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 do. 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), 4, 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), q, 0, î, ĵ, 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), 4, 0, î, ĵ, k, a, b, C, d0, E, m, p
Transcribed Image Text:Part (d) Enter an expression in Cartesian unit vector notation for a rotation, d0, 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), 9, 0, î, j, 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 do. 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), 4, 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), q, 0, î, ĵ, 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), 4, 0, î, ĵ, k, a, b, C, d0, E, m, p
Problem 5: A simple dipole consists of two charges with the same magnitude, q, but opposite sign separated by a distance d. The EDM (electric dipole moment) of E the configuration is represented by p which has a magnitude p = qd and a direction pointing from the negative charge towards the positive charge. If the dipole is located in a region with an electric field, E, then it experiences a torque T= p x E. In this problem we will explore the rotational potential energy of an electric dipole in an electric field. Part (a) Using the coordinate axes shown in the figure, express the external electric field, E, in Cartesian unit-vector notation. Expression : E = 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 (b) The EDM, p, makes an angle 0 with the positive x axis, as shown in the figure. Enter an expression for p in Cartesian unit-vector notation. Expression : p = 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 (c) Enter an expression for the torque, t, in Cartesian unit-vector notation. Expression :
Transcribed Image Text:Problem 5: A simple dipole consists of two charges with the same magnitude, q, but opposite sign separated by a distance d. The EDM (electric dipole moment) of E the configuration is represented by p which has a magnitude p = qd and a direction pointing from the negative charge towards the positive charge. If the dipole is located in a region with an electric field, E, then it experiences a torque T= p x E. In this problem we will explore the rotational potential energy of an electric dipole in an electric field. Part (a) Using the coordinate axes shown in the figure, express the external electric field, E, in Cartesian unit-vector notation. Expression : E = 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 (b) The EDM, p, makes an angle 0 with the positive x axis, as shown in the figure. Enter an expression for p in Cartesian unit-vector notation. Expression : p = 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 (c) Enter an expression for the torque, t, in Cartesian unit-vector notation. Expression :
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