A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :

(Take : e = 1.6 $$\times$$ 10^$$-$$19 C, m_p = 1.67 $$\times$$ 10^$$-$$27 kg)

An expression for oscillating electric field in a plane electromagnetic wave is given as E_z = 300 sin(5$$\pi$$ $$\times$$ 10³x $$-$$ 3$$\pi$$ $$\times$$ 10¹¹t) Vm^$$-$$1

Then, the value of magnetic field amplitude will be :

(Given : speed of light in Vacuum c = 3 $$\times$$ 10⁸ ms^$$-$$1)

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $$\Omega$$. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be :

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f₂) and new quality factor (Q₂) will be :

(f₁ = original resonant frequency, Q₁ = original quality factor)