Gate 2016 EE -SET -2 – Question 42

Energy in an electromagnetic system $$\Rightarrow E=\frac{1}{2}\lambda i=\frac{1}{2}\frac{\sqrt{i}}{g}i$$

Force in the electromagnetic system is = $$-\frac{\mathrm{d} E}{\mathrm{d} x}$$ ,where x is the air gap length(g)

$$F=-\frac{\mathrm{d} }{\mathrm{d} g}\left [ \frac{1}{2}\frac{\sqrt{i}}{g}i \right ]$$

$$F=-\left [ -\frac{1}{2}\frac{i^{\frac{3}{2}}}{g^{2}} \right ]$$

$$F=\frac{1}{2}\frac{i\frac{3}{2}}{g^{2}}$$

Substituting i = 2 and g = 0.1 into the above equation, we get F=141.4N