an 8.24 x 10-7 c charge feels a 7.89 x 10-8 n...

# Explanation: ## Step1: Recall magnetic - force formula The magnetic - force formula is $F = qvB\sin\theta$, where $F$ is the magnetic force, $q$ is the charge, $v$ is the velocity, $B$ is the magnetic - field strength, and $\theta$ is the angle between the velocity and the magnetic field. We need to solve for $B$, so we can re - arrange the formula to $B=\frac{F}{qv\sin\theta}$. ## Step2: Substitute given values Given $q = 8.24\times10^{-7}\ C$, $F = 7.89\times10^{-8}\ N$, $v = 2090\ m/s$, and $\theta = 29.4^{\circ}$. First, calculate $\sin\theta=\sin(29.4^{\circ})\approx0.49$. Then substitute into the formula: \[ \begin{align*} B&=\frac{7.89\times 10^{-8}\ N}{(8.24\times 10^{-7}\ C)\times(2090\ m/s)\times0.49}\\ &=\frac{7.89\times 10^{-8}}{8.24\times 10^{-7}\times2090\times0.49}\\ &=\frac{7.89\times 10^{-8}}{8.24\times10^{-7}\times1024.1}\\ &=\frac{7.89\times 10^{-8}}{8.438584\times10^{-4}}\\ &=\frac{7.89}{8.438584}\times10^{-8 + 4}\\ &\approx0.935\times10^{-4}\\ & = 9.35\times10^{-5}\ T \end{align*} \] # Answer: $9.35\times10^{-5}$