A proton is moving with a uniform velocity of $${{{10}^6}}$$ ms^$$-$$1 along the Y-axis, under the joint action of a magnetic field along Z-axis and an electric field of magnitude 2 $$ \times $$ 10⁴ Vm^$$-$$1 along the negative X-axis. If the electric field is switched off, the proton starts moving in a circle. The radius of the circle is nearly (given : $${e \over m}$$ ratio for proton $$ \approx $$ 10⁸ Ckg^$$-$$1)

A particle with charge e and mass m, moving along the X-axis with a uniform speed u, enters a region where a uniform electric field E is acting along the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is

An electron enters an electric field having intensity $$E = 3\widehat i + 6\widehat j + 2\widehat k$$ Vm^$$-$$1 and magnetic field having induction $$B = 2\widehat i + 3\widehat j$$ T with a velocity $$v = 2\widehat i + 3\widehat j$$ ms^$$-$$1. The magnitude of the force acting on the electron is (Given, $$e = - 1.6 \times {10^{ - 19}}$$ C)