engineering recuitment GATE IN Test Series 2023-24 Mock Test Electromagnetic Theory Magnetostatics Ampere's Circuit Law
If C is a closed curve enclosing a surface S, then the magnetic field intensity \(\vec H\) the current density \(\vec J\) and the electric flux density \(\vec D\) are related by
1
\(\mathop \int\!\!\!\int \limits_s^\; \vec H \cdot d\vec s = \mathop \oint \limits_c^\; \left( {\vec J + \frac{{\partial \vec D}}{{\partial t}}} \right) \cdot d\vec l\)
2
\(\iint\limits_c {\vec H \cdot d\vec l} =∯_s \left( {\vec J + \frac{{\partial \vec D}}{{\partial t}}} \right) \cdot d\vec s\)
3
\(∯_s\vec H \cdot d\vec s = \mathop \smallint \limits_c^\; \left( {\vec J + \frac{{\partial \vec D}}{{\partial t}}} \right) \cdot d\vec l\)
4
\(\mathop \oint \limits_c^\; \vec H \cdot d\vec l = \mathop \int\!\!\!\int \limits_s^\; \left( {\vec J + \frac{{\partial \vec D}}{{\partial t}}} \right) \cdot d\vec s\)