A steady current I is flowing in the −x direction through each of two infinitely long wires at $$y=\pm\frac L2$$ as shown in the figure. The permeability of the medium is $$\mu_0$$. The $$\overrightarrow B$$ field at (0,L,0) is

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 Ω, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B(t) = 0.25 sinωt, where ω = 2𝜋×50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is ________.

If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?

If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant of the matrix is ____________.