List of top Physics Questions on Motion in Combined Electric and Magnetic Fields asked in CBSE CLASS XII

A charged particle \(+q\) in an electric field \(\vec{E}\) experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field \(\vec{B}\). But this magnetic force is perpendicular to both velocity \(\vec{v}\) of the charged particle and the magnetic field \(\vec{B}\), so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses \(m\) and \(m_2\) having charges \(-q\) and \(+2q\) respectively. They are accelerated from rest through the same potential difference \(V\) and acquire kinetic energy \(K_1\) and \(K_2\). Then they enter in a region of uniform magnetic field \(\vec{B}\) perpendicular to their velocities.

Figure shows a narrow beam of electrons entering with a velocity of \(3\times10^7\ \text{m s}^{-1}\), symmetrically through the space between two parallel horizontal plates \(P_1P_1'\) and \(P_2P_2'\) kept \(2\ \text{cm}\) apart. If each plate is \(3\ \text{cm}\) long, calculate the potential difference \(V\) applied between the plates so that the beam just strikes the end \(P_2'\).
Figure shows a narrow beam of electrons entering with a velocity of \(3\times10^7\ \text{m s}^{-1}\), symmetrically through the space between two parallel horizontal plates \(P_1P_1'\) and \(P_2P_2'\) kept \(2\ \text{cm}\) apart. If each plate is \(3\ \text{cm}\) long, calculate the potential difference \(V\) applied between the plates so that the beam just strikes the end \(P_2'\).
A charged particle gains a speed of \(10^6 \, \text{ms}^{-1}\) when accelerated from rest through a potential difference of 10 kV. It enters a region of magnetic field of 0.4 T such that \( \vec{v} \perp \vec{B} \). The radius of the circular path described by it is:
A current of 5 A is passing along +X direction through a wire lying along X-axis. Find the magnetic field \( \vec{B} \) at a point \( \vec{r} = (3 \hat{i} + 4 \hat{j}) \, \text{m} \) due to 1 cm element of the wire, centered at the origin.
Why is Ampere’s law used for the derivation in magnetic field due to a long straight current-carrying wire of infinite length and not Biot-Savart’s law? Explain.