Hi to Maxwell

Electricity and Magnetism Level 5

An AC current $I_0 \sin(\omega t)$ with $\omega = 10^3 \text{ Hz}$ and $I_0 = 1 \text{ A}$ is flowing through a ring of radius $R$ made of material of resistivity $2.26 \times 10^8 \ \Omega \text{m}$ . Find magnitude of magnetic field at the centre of the ring at the instant the current in ring is zero.

NOTE: The material obeys ohm's law.

HINT: Modified ampere's law.

\frac{\mu_0}{2R}

Answer is non-zero and independant of

R

\frac{\mu_0}{R}

zero

1 solution

A Former Brilliant Member
Jan 9, 2017

Value of magnetic field at the centre of ring is $\huge{\frac{\mu_0(I+\epsilon_0 \rho \ dI/dt)}{2R}}$ {Latter part is displacement current-Maxwell's correction}. putting values we get $\epsilon_0\rho$ =2. Therefore answer is $\boxed{\frac{\mu_0}{R}}$

With the numbers in the problem the power dissipation in the coil is 100 MW. This is impossible to maintain. That's is why the effect described in this problem is never observed.

Laszlo Mihaly - 3 years, 8 months ago

Yes, the values in problem are adjusted to make the resultant effect of modified ampere's law is considerable. In real world the effect is not easily observed.

A Former Brilliant Member - 3 years, 7 months ago

Hi to Maxwell

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