If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?
A) 71 N/C
B) 56 N/C
C) 60 N/C
D) 53 N/C
E) 67 N/C

Question

If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P? 
A) 71 N/C 
B) 56 N/C 
C) 60 N/C 
D) 53 N/C 
E) 67 N/C

Quizplus · Accepted Answer

First, we need to find the distance from point P to each charge. Using the Pythagorean Theorem, we find that the distance from point P to Q is approximately 85 cm and the distance from point P to q is approximately 100 cm. 
Next, we can use the formula for the electric field due to a point charge: 
$E = \frac{kq}{r^2}$, 
where k is Coulomb's constant (9 × 10^9 N·m^2/C^2), q is the charge, and r is the distance from the charge to the point where we want to find the electric field. 
Using this formula for each charge, we get: 
$E_Q = \frac{(9 	imes 10^9)(6 	imes 10^{-9})}{(0.85)^2} ≈ 54 N/C$
and 
$E_q = \frac{(9 	imes 10^9)(3 	imes 10^{-9})}{(1)^2} = 27 N/C$
Note that the electric field due to q points to the left, while the electric field due to Q points to the right. Therefore, we need to subtract the electric field due to q from the electric field due to Q to get the total electric field at point P: 
$E_{net} = E_Q - E_q ≈ 54 - 27 = 27 N/C$ 
However, we must also take into account the fact that the electric field due to Q and q are at an angle to each other. We can resolve the electric field due to Q and q into their x and y components, using trigonometry. The x-component of $E_Q$ balances out the x-component of $E_q$, since they point in opposite directions. So, we only need to add the y-component of $E_Q$ to the y-component of $E_q$: 
$E_{net} = \frac{(9 	imes 10^9)(6 	imes 10^{-9})\sin(37^\circ)}{(0.85)^2} + \frac{(9 	imes 10^9)(3 	imes 10^{-9})\sin(53.13^\circ)}{(1)^2} ≈ 53 N/C$ 
Therefore, the magnitude of the electric field at point P is approximately 53 N/C, which corresponds to answer choice D.

If a = 60 Cm, B = 80 Cm, Q