A single loop has flux changing from \(0.030\,\mathrm{Wb}\) to \(0.010\,\mathrm{Wb}\) in \(0.20\,\mathrm{s}\). Find the magnitude of the average induced emf.

A \(50\)-turn coil has flux per turn changing at \(3.0\times10^{-3}\,\mathrm{Wb\,s^{-1}}\). Find \(|\mathcal E|\).

A loop of area \(0.080\,\mathrm{m^2}\) is perpendicular to a field increasing at \(0.60\,\mathrm{T\,s^{-1}}\). Find the induced emf magnitude.

A \(120\)-turn coil has area \(2.0\times10^{-3}\,\mathrm{m^2}\). It is perpendicular to a field decreasing at \(4.0\,\mathrm{T\,s^{-1}}\). Find \(|\mathcal E|\).

A coil has \(N=40\), \(A=0.015\,\mathrm{m^2}\), and \(\theta=60^\circ\). The field changes at \(2.0\,\mathrm{T\,s^{-1}}\). Find \(|\mathcal E|\).

A loop has area increasing at \(0.020\,\mathrm{m^2\,s^{-1}}\) in a steady perpendicular \(0.30\,\mathrm{T}\) field. Find \(|\mathcal E|\).

A \(200\)-turn coil has average emf magnitude \(3.0\,\mathrm{V}\) while the flux per turn changes uniformly for \(0.50\,\mathrm{s}\). Find the magnitude of the flux change per turn.

A coil's flux per turn is \(\Phi_B(t)=0.020t^2\) in webers. If \(N=10\), find \(\mathcal E(t)\).

A loop rotates in a uniform field with \(\theta=\omega t\). If \(\Phi_B=BA\cos\omega t\), derive \(\mathcal E(t)\) for one turn.

A \(80\)-turn coil of area \(0.010\,\mathrm{m^2}\) rotates at \(30\,\mathrm{rad\,s^{-1}}\) in a \(0.20\,\mathrm{T}\) field. Find the peak emf.

A square loop of side \(0.20\,\mathrm{m}\) enters a uniform \(0.60\,\mathrm{T}\) field at \(0.50\,\mathrm{m\,s^{-1}}\). While partly entering, find the emf magnitude.

A field changes according to \(B(t)=0.10+0.50t\) through a fixed perpendicular loop of area \(0.040\,\mathrm{m^2}\). Find the induced emf.

A student multiplies \(N\) by total coil area and also by flux per turn. Explain the double-counting error.

A \(25\)-turn coil has flux per turn \(\Phi_B=0.012\cos(100t)\,\mathrm{Wb}\). Find the emf function.

A loop area decreases linearly from \(0.050\,\mathrm{m^2}\) to \(0.020\,\mathrm{m^2}\) in \(0.30\,\mathrm{s}\) in a steady perpendicular \(0.80\,\mathrm{T}\) field. Find the average emf magnitude.

A coil has \(N\), area \(A\), and rotates with angular speed \(\omega\) in field \(B\). Derive the rms emf if \(\Phi_B=BA\cos\omega t\).

A loop crosses a field boundary. Its flux is \(\Phi_B=Bhx(t)\). Derive the emf in terms of \(B\), \(h\), and \(dx/dt\).

A coil has \(N=100\), \(A=0.0040\,\mathrm{m^2}\), and \(B(t)=0.30e^{-2t}\). The coil is perpendicular to the field. Find \(\mathcal E(t)\).

A flat loop in a uniform field has \(B\), \(A\), and \(\theta\) all time-dependent. Write the full derivative for \(\mathcal E\) from \(\Phi_B=BA\cos\theta\).

A coil's measured emf is zero at an instant even though it is rotating in a magnetic field. Explain how this can happen using \(\mathcal E=NBA\omega\sin\omega t\).