Answer to Question #259369 in Electricity and Magnetism for ops

Question

An object having a mass of 10 g and a charge of + 8.0x10^-5 C is placed in an electric field defined by Ex = 3.0x10^3 N/C, Ey = - 6000 N/C, and Ez = 0. (a) What are the magnitude and direction of the force on the object? (b) If the object starts from rest at the origin, what will be its coordinates after 3.0 s?

Answer 1

Mass(m)=10g

Charge (wa)=$8.0\times10^{-5}C$

Electric field

$$E_x=3\times10^{3}N/C,E_y=-{6000}N/C,E_z=0N/C$$

$E=E_x\hat{i}+E_y\hat{j}+E_z\hat{k}$

$E=3000\hat{i}-6000\hat{j}+0\hat{k}$

Force

$F=qE$

$$F=8.0\times10^{-5}\times(3000\hat{i}-6000\hat{j}+0\hat{k})$$

$F=(0.24\hat{i}-0.48\hat{j} )N$

$$|F|=\sqrt{(0.24^2++(-0.48)^2}=\sqrt{0.288}=0.5366N$$

Direction

$$\theta=tan^{-1}(\frac{-0.48}{0.24})=tan^{-1}({-2})=-63.43°$$

Part(b)

Force (F)=ma

$a=\frac{F}{m}$

$a=\frac{0.5366}{10^{-2}}=53.66m/sec$

We know that

$S=ut+\frac{1}{2}at^2$

$$X=0+\frac{1}{2}\times53.66\times3^2=241.47 m$$