Question

The electric field in a region is uniform (constant in space) and given by E-( 148.0 1 -110.03)N/C. An additional charge 10.4 nC (nano-coulombs) is placed into this region. What is the y component of the electric force on this charge?

Answer 1

The y-component of the electric force on this charge is
`F_y = -1.144* 10^(-6)\ N.`

Step-by-step explanation:

Given:

• Electric field in the region,
  `\vec E = (148.0\ \hat i-110.0\ \hat j)\ N/C.`
• Charge placed into the region,
  `q = 10.4\ nC = 10.4* 10^(-9)\ C.`

where,
`\hat i,\ \hat j` are the unit vectors along the positive x and y axes respectively.

The electric field at a point is defined as the electrostatic force experienced per unit positive test charge, placed at that point, such that,

`\vec E = (\vec F)/(q)\\\therefore \vec F = q\vec E\\=(10.4* 10^(-9))* (148.0\ \hat i-110.0\ \hat j)\\=(1.539* 10^(-6)\ \hat i-1.144* 10^(-6)\ \hat j)\ N.`

Thus, the y-component of the electric force on this charge is
`F_y = -1.144* 10^(-6)\ N.`