State Faraday's law in field form.

A circular path of radius \(0.20\,\mathrm{m}\) has uniform tangential induced field \(0.30\,\mathrm{V\,m^{-1}}\). Find the emf around the path.

A uniform magnetic field changes at \(4.0\,\mathrm{T\,s^{-1}}\) inside a circular region. Find the induced electric field magnitude at \(r=0.10\,\mathrm{m}\) inside the region.

A changing magnetic field is confined to radius \(R=0.30\,\mathrm{m}\) and changes at \(2.0\,\mathrm{T\,s^{-1}}\). Find \(E\) at \(r=0.60\,\mathrm{m}\).

Explain why an induced electric field can exist even where there is no wire.

Why is an induced electric field from changing magnetic flux nonconservative?

Inside a radius \(R\) where \(dB/dt\) is uniform, derive \(E=(r/2)|dB/dt|\).

Outside a changing-field region of radius \(R\), derive \(E=(R^2/2r)|dB/dt|\).

A changing magnetic field into the page is increasing. What is the direction of the induced electric field lines?

A changing magnetic field out of the page is increasing. What is the direction of the induced electric field lines?

For a circular path inside a changing-field region, if \(r\) doubles, how does \(E\) change?

For a circular path outside a changing-field region, if \(r\) doubles, how does \(E\) change?

At \(r=R\), show that the inside and outside circular-field formulas agree.

A circular electron orbit of radius \(0.050\,\mathrm{m}\) lies inside a region where \(B\) changes at \(8.0\,\mathrm{T\,s^{-1}}\). Find the induced electric force magnitude on an electron.

A circular path of radius \(0.25\,\mathrm{m}\) has emf magnitude \(0.50\,\mathrm{V}\). Find the average tangential induced electric field.

A changing field is uniform inside radius \(R\). Sketch verbally how \(E(r)\) varies from \(r=0\) to far outside the region.

Explain why voltage between two points is path-dependent for an induced electric field.

A circular region has \(B(t)=B_0+kt\) into the page. Determine whether the induced electric field direction is clockwise or counterclockwise for \(k>0\).

For \(r<R\), derive the acceleration magnitude of a charge \(q\), mass \(m\), released at radius \(r\) by a changing magnetic field \(dB/dt\).

Use Faraday's law to explain why induced electric field lines cannot be purely radial around the axis of a changing uniform magnetic field.