Electric Fields and Capacitors: Practice Questions

A straight wire of length \(0.15 \text{ m}\) carries a current of \(2.0 \text{ A}\) perpendicular to a uniform magnetic field of flux density \(0.40 \text{ T}\). What is the magnitude of the magnetic force acting on the wire?

An electron enters a uniform magnetic field of flux density \( 0.025 \text{ T} \) at a speed of \( 4.0 \times 10^6 \text{ m s}^{-1} \). The velocity of the electron is perpendicular to the magnetic field. What is the radius of the circular path followed by the electron?

A horizontal wire of length \(L\) and mass \(M\) is placed in a uniform horizontal magnetic field of flux density \(B\) which is perpendicular to the wire. A current \(I\) is passed through the wire such that the magnetic force exactly balances the weight of the wire. If the current is doubled and the magnetic flux density is halved, what must happen to the length of the wire to maintain this balance?

A potential difference of 600 V is applied across two parallel metal plates separated by a distance of 4.0 cm. What is the magnitude of the electric field strength between the plates?

A capacitor of capacitance \(C\) is charged by a battery of e.m.f. \(V\). The battery is then disconnected, and the capacitor is connected in parallel with an identical uncharged capacitor of capacitance \(C\). What is the total energy stored in the two-capacitor system compared to the initial energy stored in the first capacitor?

Calculate the magnitude of the magnetic force acting on an electron moving at a velocity of \( 4.0 \times 10^{6} \text{ m s}^{-1} \) perpendicular to a uniform magnetic field of flux density \( 0.25 \text{ T} \).
(Charge of an electron \( e = 1.6 \times 10^{-19} \text{ C} \))