Answer
${\bf 1.25}\;\rm T$
Work Step by Step
We know that the force exerted by a magnetic field on a moving charges is given by
$$F=q\vec v\times \vec B =qvB\sin90^\circ=qvB$$
And the charged particles here are the protons that have undergone a uniform circular motion at a constant speed of $0.1c$ where $c$ is the speed of light.
So,
$$F=\dfrac{mv^2}{R}=evB$$
Hence, the magnetic electric field needed is given by
$$B=\dfrac{mv }{eR}$$
Plug the known;
$$B=\dfrac{(1.67\times 10^{-27})(0.1\times 3\times 10^8)}{(1.6\times 10^{-19})(0.25)}$$
$$B=\color{red}{\bf 1.25}\;\rm T$$
