A \(0.50\,\mathrm{m}\) rod moves at \(4.0\,\mathrm{m\,s^{-1}}\) perpendicular to a \(0.30\,\mathrm{T}\) field. Find the motional emf.

A rod has motional emf \(1.2\,\mathrm{V}\) while moving at \(3.0\,\mathrm{m\,s^{-1}}\) through a \(0.80\,\mathrm{T}\) field. Find its length.

A \(0.25\,\mathrm{m}\) rod moves at \(6.0\,\mathrm{m\,s^{-1}}\) in a \(0.40\,\mathrm{T}\) field. The circuit resistance is \(3.0\,\Omega\). Find the induced current.

Positive charges in a rod move with velocity \(\vec v\) to the right through a magnetic field into the page. Which end of the rod becomes positive if the rod is vertical?

A rod of length \(0.60\,\mathrm{m}\) moves at \(5.0\,\mathrm{m\,s^{-1}}\), but only the velocity component perpendicular to the rod and field is \(3.0\,\mathrm{m\,s^{-1}}\). If \(B=0.20\,\mathrm{T}\), find \(|\mathcal E|\).

A sliding rod has \(B=0.50\,\mathrm{T}\), \(\ell=0.40\,\mathrm{m}\), \(v=2.0\,\mathrm{m\,s^{-1}}\), and total resistance \(0.80\,\Omega\). Find the magnetic drag force.

For the rod in the previous style of setup, derive \(F=B^2\ell^2v/R\) for the magnetic drag force.

Show that the mechanical power needed to pull a sliding rod at constant speed equals the electrical power dissipated.

A rod moves on rails so the loop area is \(A=\ell x\). If \(x=vt\), derive the emf magnitude from Faraday's law.

A \(0.30\,\mathrm{m}\) rod moves through a \(0.90\,\mathrm{T}\) field at unknown speed. The emf is \(0.81\,\mathrm{V}\). Find the speed.

A rod moves parallel to a magnetic field. What is the motional emf across the rod?

A vertical rod moves right through a field out of the page. Which end becomes positive?

A rod of length \(\ell\) rotates about one end with angular speed \(\omega\) in a uniform field perpendicular to the plane of rotation. Derive the emf between its ends.

A \(0.50\,\mathrm{m}\) rod rotates about one end at \(12\,\mathrm{rad\,s^{-1}}\) in a perpendicular \(0.20\,\mathrm{T}\) field. Find the emf between its ends.

A sliding rod circuit has resistance \(R\). If its speed doubles, by what factors do emf, current, drag force, and dissipated power change?

A sliding rod in a field is pulled by a constant external force. Explain why it can reach a terminal speed.

Find the terminal speed of a sliding rod pulled by constant force \(F\) in field \(B\), length \(\ell\), and circuit resistance \(R\).

A rod of length \(\ell\) moves with velocity making angle \(\alpha\) to the direction perpendicular to the rod and field. Write the emf magnitude.

A conducting rod moves in a magnetic field but is not part of a closed circuit. Explain what is still physically present.

A sliding rod of mass \(m\) starts at speed \(v_0\) with no external pull. The magnetic drag force is \(F=-(B^2\ell^2/R)v\). Derive \(v(t)\).