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- https://phys.libretexts.org/Courses/Muhlenberg_College/Physics_122%3A_General_Physics_II_(Collett)/09%3A_Electromagnetic_Induction/9.04%3A_Motional_EmfMagnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantit...Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantities varies, a corresponding variation in magnetic flux occurs. So far, we’ve only considered flux changes due to a changing field. Now we look at another possibility: a changing area through which the field lines pass including a change in the orientation of the area.
- https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/23%3A_Electromagnetic_Induction/23.02%3A_Induction_in_a_Moving_ConductorWe can calculate the flux of the magnetic field through the loop at some time \(t\): \[\begin{aligned} \Phi_B(t) = \vec B \cdot \vec A = (B\hat x) \cdot (\cos(\omega t) \hat x -\sin(\omega t)\hat z)=A...We can calculate the flux of the magnetic field through the loop at some time \(t\): \[\begin{aligned} \Phi_B(t) = \vec B \cdot \vec A = (B\hat x) \cdot (\cos(\omega t) \hat x -\sin(\omega t)\hat z)=AB\cos(\omega t)\end{aligned}\] where we did not use the integral for the flux, since the magnetic field is constant over the area of the loop.
- https://phys.libretexts.org/Courses/Grand_Rapids_Community_College/PH246_Calculus_Physics_II_(2025)/09%3A_Electromagnetic_Induction/9.04%3A_Motional_EmfMagnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantit...Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantities varies, a corresponding variation in magnetic flux occurs. So far, we’ve only considered flux changes due to a changing field. Now we look at another possibility: a changing area through which the field lines pass including a change in the orientation of the area.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/08%3A_Electromagnetic_Induction/8.02%3A_Motional_EmfThe magnetic force on the infinitesimal segment of length dx shown in part (c) of Figure \(\PageIndex{6}\) is \(dF_m = IBdx\), so the magnetic torque on this segment is \[d\tau_m = x \cdot dF_m = IBxd...The magnetic force on the infinitesimal segment of length dx shown in part (c) of Figure \(\PageIndex{6}\) is \(dF_m = IBdx\), so the magnetic torque on this segment is \[d\tau_m = x \cdot dF_m = IBxdx.\] The net magnetic torque on the rod is then \[\tau_m = \int_0^r d\tau_m = IB \int_0^r x \, dx = \frac{1}{2}IBr^2.\] The torque \(\tau\) that you exert on the rod is equal and opposite to \(\tau_m\), and the work that you do when the rod rotates through an angle \(d\theta\) is \(dW = rd\theta\).
- https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/23%3A_Electromagnetic_Induction/23.02%3A_Induction_in_a_Moving_ConductorWe can calculate the flux of the magnetic field through the loop at some time \(t\): \[\begin{aligned} \Phi_B(t) = \vec B \cdot \vec A = (B\hat x) \cdot (\cos(\omega t) \hat x -\sin(\omega t)\hat z)=A...We can calculate the flux of the magnetic field through the loop at some time \(t\): \[\begin{aligned} \Phi_B(t) = \vec B \cdot \vec A = (B\hat x) \cdot (\cos(\omega t) \hat x -\sin(\omega t)\hat z)=AB\cos(\omega t)\end{aligned}\] where we did not use the integral for the flux, since the magnetic field is constant over the area of the loop.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/22%3A_Induction_AC_Circuits_and_Electrical_Technologies/22.1%3A_Magnetic_Flux_Induction_and_Faradays_LawFaraday’s law of induction states that an electromotive force is induced by a change in the magnetic flux.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/13%3A_Electromagnetic_Induction/13.04%3A_Motional_EmfMagnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantit...Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantities varies, a corresponding variation in magnetic flux occurs. So far, we’ve only considered flux changes due to a changing field. Now we look at another possibility: a changing area through which the field lines pass including a change in the orientation of the area.
- https://phys.libretexts.org/Courses/Kettering_University/Electricity_and_Magnetism_with_Applications_to_Amateur_Radio_and_Wireless_Technology/09%3A_Electromagnetic_Induction/9.05%3A_Motional_Source_VoltageMagnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantit...Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the orientation of the field with the surface area. If any of these quantities varies, a corresponding variation in magnetic flux occurs. So far, we’ve only considered flux changes due to a changing field. Now we look at another possibility: a changing area through which the field lines pass including a change in the orientation of the area.
