An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connected to a $$230$$ $$V,$$ $$50$$ $$Hz$$ ac supply. Neglect coil resistance, core loss, iron reluctance and leakage inductance. $$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,H/m} \right)$$

The average force on the core to reduce the air gap will be

An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connected to a $$230$$ $$V,$$ $$50$$ $$Hz$$ ac supply. Neglect coil resistance, core loss, iron reluctance and leakage inductance. $$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,H/m} \right)$$

The current in the inductor is

Divergence of the vector field $$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\;y^2\right)\widehat k$$$ is

Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right) + {x^2} + {y^2}} \right]\widehat k\,\,$$