Calculation of the average coefficient of magnetic induction in an ­ medium with a fine-grained metal-dielectric structure is encountered in many applied problems. Including in those cases when at some points in time it is possible to measure the change in the electromagnetic field and the gradients of its components at the boundary of the ­ domain, but it is impossible to measure this field inside ­ even at some point in time. In this case, the problem of calculating the averaged magnetic induction coefficient leads to the search for a solution to a nonclassical boundary value problem for a hyperbolic equation in the absence of initial data, but with the measured values of the electromagnetic field and the gradients of its components at the boundary or part of the boundary of the ­ domain. If the ­ domain is one-dimensional, the solution to such a nonclassical problem is the solution of some integral equation of the second kind, which is uniquely solvable in the class of smooth functions. This work was supported by the Russian Foundation for Basic Research (grant 20-01-00469).