Respuesta :
The electric field at the point P which has coordinates (0,0. 40)m is [1.1×10⁵i +2.5×10⁵j ]N/C.
What is electric field?
The electric field is the region of space where an object experiences electric force of attraction or repulsion.
E₁ is the electric field due to q₁ =7μC at origin and E₂ is the field due to q₂ = −5μC at (0,0.40)m
E₁ =kq₁/r₁²
E₁ =9×10⁹ ×7×10⁻⁶ /(0.40)²
E₁ =3.93×10⁵ N/C
E₂ =kq₂/r₂²
E₂=9×10⁹ ×5×10⁻⁶ /(0.50)²
E₂=1.8×10⁵ N/C
The distance between q₂ and point P, r₂= √[(0.30)² +(0.40)²] =0.50m
Referring to the figure, sinθ= 0.40/0.50 =4/5 and cosθ= 0.30/0.50 = 3/5
The vector E₁ has only y component.
The Electric field has x component given by E₂ cosθ=3/5E₂ and a negative y component given by −E₂ sinθ = -4/5 E₂
Electric field in vector form is,
E₁ =3.93×10⁵ jN/C
E₂ =[1.08 i +(−1.44 j)]×10⁵ N/C
E = E₁ + E₂
E =[1.08×10⁵i +(3.9−1.44)×10⁵j]N/C
E =[1.1×10⁵i +2.5×10⁵j ]N/C
Thus, the electric field at the point p which has coordinates (0,0. 40)m is [1.1×10⁵i +2.5×10⁵j ]N/C.
Learn more about electric field.
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