Question

Reference : Physics for Scientist and Engineers Chapter 21.

Two point charges q1 = 2 C and q2 = - 5 C are located in the (x,y) plane at coordinates (2,0) m and (-3,0) m respectively. Find:

a) The electric field created for both charges at points (0,0), (5,0) and (0,2)

b) the electric force on a point charge of -2.00 C placed at points (0,0), (5,0) and (0,2)

Answer 1

a)

At (0,0)

Electric field by charge q₂ at A is given as

E₂ = k q₂/AB²

E₂ = (9 x 10⁹) (5)/ (3)²

E₂ = 5 x 10⁹ N/C       towards left

Electric field at (0,0 )by charge q₁ at C is given as

E₁ = k q₂/BC²

E₁ = (9 x 10⁹) (2)/ (2)²

E₁ = 4.5 x 10⁹ N/C       towards left

Total Electric field at B

E = E₁ + E₂ = 5 x 10⁹ + 4.5 x 10⁹ = 9.5 x 10⁹ N/C          towards left

Electric force on charge -2 C placed at (0,0) = F = qE = 2 x 9.5 x 10⁹ = 19 x 10⁹ N towards right

At D(5,0)

Electric field by charge q₂ at A is given as

E₂ = k q₂/AD²

E₂ = (9 x 10⁹) (5)/ (8)²

E₂ = 0.703 x 10⁹ N/C       towards left

Electric field at (0,0 )by charge q₁ at C is given as

E₁ = k q₂/CD²

E₁ = (9 x 10⁹) (2)/ (3)²

E₁ = 2 x 10⁹ N/C       towards right

Since E₁ and E₂ are in opposite direction

Total Electric field at B

E = E₁ - E₂ = 2 x 10⁹ - 0.703 x 10⁹ = 1.297 x 10⁹ N/C          towards right

Electric force on charge -2 C placed at (0,5) = F = qE = 2 x 1.297 x 10⁹ = 2.594 x 10⁹ N towards left

In triangle ABE

AE = sqrt (AB² + BE²) = sqrt (3² + 2²) = 3.61

Similarly , CE = 2.83

₁ = tan^-1(BE/BC) = tan^-1(2/2) = 45

₂ = tan^-1(BE/AB) = tan^-1(2/3) = 33.7

At (0,2)

Electric field by charge q₂ at A is given as

E₂ = k q₂/AE²

E₂ = (9 x 10⁹) (5)/ (3.61)²

E₂ = 3.45 x 10⁹ N/C      

Electric field at (0,2 )by charge q₁ at C is given as

E₁ = k q₂/CE²

E₁ = (9 x 10⁹) (2)/ (2.83)²

E₁ = 2.25 x 10⁹ N/C     

total electric field along X-direction = E₁ Cos1 + E₂ Cos2 = (2.25 x 10⁹) Cos45 + (3.45 x 10⁹ ) Cos33.7

E_x = 4.46 x 10⁹ N/C

total electric field along Y-direction = E₁ Sin1 - E₂ Sin2 = (2.25 x 10⁹) Sin45 - (3.45 x 10⁹ ) Sin33.7

E_y = - 0.323 x 10⁹ N/C

net electric field = E = sqrt(Ex2 + Ey2) = sqrt((4.46 x 10⁹)² + (- 0.323 x 10⁹)²) = 4.47 x 10⁹ N/C

Electric force on charge -2 C placed at (0,2) = F = qE = 2 x 4.47 x 10⁹ = 8.94 x 10⁹ N