In the last few years, it has been found that transverse waves are present at all times in coronal loops or spicules. Their energy has been estimated with an expression derived for bulk Alfvén waves in homogeneous media, with correspondingly uniform wave energy density and flux. The kink mode, however, is localized in space with the energy density and flux dependent on the position in the cross-sectional plane. The more relevant quantities for the kink mode are the integrals of the energy density and flux over the cross-sectional plane. The present paper provides an approximation to the energy propagated by kink modes in an ensemble of flux tubes by means of combining the analysis of single flux tube kink oscillations with a filling factor for the tube cross-sectional area. This finally allows one to compare the expressions for energy flux of Alfvén waves with an ensemble of kink waves. We find that the correction factor for the energy in kink waves, compared to the bulk Alfvén waves, is between f and 2f , where f is the density filling factor of the ensemble of flux tubes.

Context. Rapidly damped transverse oscillations of coronal loop systems are often observed. Aims. We aim to study analytically the resonantly damped oscillations of a system of two not necessarily identical coronal loops and their dependence on the equilibrium parameters, improving on and extending the results for two identical coronal loops. Methods. The linearised magnetohydrodynamic equations for a cold plasma were solved in the long-wavelength limit and for thin boundary layers in bicylindrical coordinates. We investigated the effects of the density contrast between the two loops, the thickness of their inhomogeneous layers, and the separation distance between them. The complex spectrum was also studied. Results. We obtained more general expressions for the linear damping rate of the transverse oscillations in a system of two coronal loops. The results can be reduced to expressions found previously for the special cases of one vanishing loop or two identical loops. The interaction between the loops results in a stronger damping of the high-frequency eigenoscillation in comparison with that of the low-frequency eigenoscillation. By decreasing the distance between loops, the efficiency of resonant damping is reduced.

We investigated the influence of context on students' understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third version was without physics context. We administered the tests to 216 first-year pre-med students at a Belgian (Flemish) university. We found that students perform significantly better in the context of the Lorentz force. Students more often chose the incorrect alternative corresponding to the vector sum in the test versions involving an electric dipole or without physics context when the vectors are not orthogonal. For orthogonal vectors, a sign error-i.e., inverting the direction of the resulting vector-was the most common mistake in both tests with physics context, while without physics context selecting the alternative corresponding to the sum remained the most common mistake. Prior familiarity with a right-hand rule in a specific context seems to be able to explain improved scores in the test version concerning the Lorentz force. Instructors and curriculum developers can benefit from adopting an integrated approach in which the mathematical aspects of the cross product are treated together with multiple examples in physics, allowing students to transition from using specific rules to determine a cross product, to a more integrated understanding of it.

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