Question

Find the x and y components of the electric field produced by q_1 and q_2 in Fig. 17-53 at (a) point A: (b) point B.

Answer 1

According to the given problem,

For point A E_x comes from q₁ [positve]and is directed to the right

So E_x = k*q₁/r² = 9.0*10⁹*2*10^-6/2² = 4500N/C

E_y comes from q₂ [negative]and is directed upward

So E_y = k*q₂/r² = 9.0*10⁹*1*10^-6/2² = 2250N/C

For point B:

E_x comes from both q₁ & q₂

from q₁ the x field is to the right

E_x1 = k*q1/r² = 9*10⁹*2*10^-6/4² = 1125 N/C

q₂ contributes both an x & y component

r for this charge is √(2² + 2²) = 2.828m and the angle it makes with the x axis is 135^o (since the field is toward q2

so E_x2 = k*q₂/r²*cos(θ) = 9.0*10⁹*1*10^-6/2.828²*cos(135^o) = -795.5 N/C

and E_y2 = k*q₂/r²*sin(θ) = 9.0*10⁹*1*10^-6/2.828²*sin(135^o) = 795.5 N/C

So E_x = E_x1 + E_x2 = 329.5N/C

and E_y = 795.5N/C