A coil of inductance 1.0 H and resistance 100 Omega is connected to a battery of emf 12 V. Find the energy stored in the magnetic field associated with the coil at an instant 10 ms after the circuit is switched on.

Explanation

Time constant of circuiti is `tau = (L)/(R ) =(1.0)/(100) = 10^(-2)s`
As `I = I_(0) (1 - e^(-t//tau)) = (E _(0))/(R ) (1 - e^(-t//tau`)
`:. I = (12)/(100) (1 - e^(-10^(-2_(//10^(-2)))))`
` = 0.12 (1 - (1)/(e)) = 0.0758 A`
Energy store `= (1)/(2) LI^(2) = (1)/(2) xx 1.0 (0.0758)^(2)`
`= 2.87 xx 10^(-3) J`
Maximum electric intnesity the capacitor can withstand = 10% dielectric strength
i.e., `E = (10)/(100) xx 3.0 xx 10^(6) = 3 xx 10^(5) V//,`
`d = 1 mm = 10^(-3) m`