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The magnetoelectric effect due to a semispherical capacitor surrounded by a spherical topologically insulating shell

We consider the magnetoelectric effect produced by a capacitor formed by two semispherical perfectly conducting plates subjected to a potential difference and surrounded by a spherical shell of a topologically insulating material. The modified Maxwell equations are solved in terms of coupled electric and magnetic scalar potentials using spherical coordinates and in the approximation where the effective magnetoelectric coupling is of the order of the fine structure constant. The emphasis is placed in the calculation of the magnetic field for several relevant configurations designed to enhance the possibility of measuring this field. The magnitudes we obtain fall within the sensitivities of magnetometers based upon nitrogen-vacancy centers in diamond as well as of devices using scanning SQUID magnetometry.