Answer
$B=3.3T$
Work Step by Step
$B=\frac{\gamma mv}{rq}$
$998GeV\times\frac{1.60^{-10}J}{1GeV}=1.60\times10^{-7}J$
$E_k=\Bigg(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\Bigg)mc^2$
$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{E_k}{mc^2}+1$
$\frac{1}{1-\frac{v^2}{c^2}}=\bigg(\frac{E_k}{mc^2}+1\bigg)^2$
$\frac{v^2}{c^2}=1-\frac{1}{\bigg(\frac{E_k}{mc^2}+1\bigg)^2}$
$v=c\sqrt{1-\frac{1}{\bigg(\frac{E_k}{mc^2}+1\bigg)^2}}$
$\bigg(\frac{E_k}{mc^2}+1\bigg)^2=\bigg(\frac{1.60\times10^{-7}J}{(1.67\times10^{-27}kg)(2.998\times10^8\frac{m}{s})^2}+1\bigg)^2=1.14\times10^6$
$v=0.999999c$
$\gamma=\frac{1}{\sqrt{1-(0.999999)^2}}=754$
$B=\frac{\gamma mv}{rq}=\big(\frac{K}{mc^2}-1\big)mc$
$=\big(\frac{998GeV}{0.938GeV}-1\big)(1.67\times10^{-27}kg)(2.998\times10^8\frac{m}{s})$
$=3.3T$
