Question

In a given region, there exists an electric field,

E=(2 x+ z) ̂ i+ ( x−y) ̂ j+ (2 z−y)k̂ N/m⋅C .

a. Determine the force felt by a 2.0C charge is placed at position (3.25, 7.5, -4.0) m.

b. Determine the position of a 2.0C charge that feels a force of 15̂j N

Answer 1

E=(2 x+ z) ̂ i+ ( x−y) ̂ j+ (2 z−y)k̂ N/mC .

a)
Q = 2 C = 2000 mC
F = Q*E
= 2000 mC*{ (2 x+ z) ̂ i+ ( x−y) ̂ j+ (2 z−y)k̂ N/mC}
= 2000*{(2 *3.25 -4) ̂ i+ ( 3.25−7.5) ̂ j+ (2*-4 − 7.5)k̂ N/mC}
= 2000*{2.6 i -4.25 j - 15.5 k }
= 5200 i -8500 j - 31000 k N

magnitude of F = sqrt (5200^2 + 8500^2 + 31000^2)
= 32562 N

b)
Force is in j direction only
2x+z = 0 ---> x = -z/2
2z-y = 0 ----> y = 2z

for y componenet,
Q*Ey = Fy
2000*(x-y) = 15
(x-y) = 7.5*10^-3
(-z/2 - 2z) = 7.5*10^-3
z(-1/2 - 2) = 7.5*10^-3
z (-5/2) = 7.5*10^-3
z = -3.0*10^-3 m
x = 1.5*10^-3 m
y = -6.0*10^-3 m

Point is:
(1.5,-6,3) mm