Background pertinent to this problem is available in Interactive LearningWare 18.3. A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 4900 N/C and is directed in the positive x direction. A point charge -6.9 × 10-9 C is placed at the origin. Find the magnitude of the net electric field at (a) x = -0.19 m, (b) x = +0.19 m, and (c) y = +0.19 m
Not too sure how to go about this question
Steven/Arlo/Carlos/Manny -- pick one name and use it. Name-games are just silly here.
To find the magnitude of the net electric field at different points in the x, y plane, we can break down the problem into two parts: the electric field due to the point charge, and the electric field due to the uniform electric field.
1. Electric field due to the point charge:
The electric field due to a point charge at a given location is given by Coulomb's Law:
E_point = k * (q/r^2)
Where:
- E_point is the electric field due to the point charge,
- k is Coulomb's constant (8.99 x 10^9 N m^2/C^2),
- q is the magnitude of the point charge (-6.9 x 10^-9 C),
- r is the distance from the charge to the point where we want to find the electric field.
In this case, we want to find the electric field at specific points in the x, y plane. So, we need to find the distance (r) from the origin to each of these points.
2. Electric field due to the uniform electric field:
The electric field due to a uniform electric field is constant throughout. Given that the electric field has a magnitude of 4900 N/C and is directed in the positive x direction, we know the electric field will be the same at every point in the x, y plane. Therefore, we can directly use this value to calculate the electric field without having to calculate distances.
To determine the net electric field at a point, we need to add the electric fields due to the point charge and the uniform electric field vectors.
Now, let's calculate the magnitude of the net electric field at each of the given points:
(a) x = -0.19 m:
To find the net electric field, we first calculate the electric field due to the point charge, and then add it to the electric field due to the uniform electric field.
1. Electric field due to the point charge at the origin:
E_point_origin = k * (q/r^2)
= (8.99 x 10^9 N m^2/C^2) * (-6.9 x 10^-9 C) / (0 m)^2
Since the point is at the origin, the distance (r) is zero, and hence the denominator becomes zero. As a result, the electric field due to the point charge at the origin is undefined.
2. Electric field due to the uniform electric field:
E_uniform = 4900 N/C
To calculate the net electric field at x = -0.19 m, we need to add the electric field due to the point charge and the electric field due to the uniform electric field:
E_net_x_minus = E_uniform + E_point_origin
But since the electric field due to the point charge at the origin is undefined, we cannot determine the net electric field at x = -0.19 m.
(b) x = +0.19 m:
The process is the same as in part (a), but this time we find the electric field due to the point charge at the specific location.
1. Electric field due to the point charge at the given location:
E_point_location = k * (q/r^2)
= (8.99 x 10^9 N m^2/C^2) * (-6.9 x 10^-9 C) / (0.19 m)^2
Calculate this value using your calculator or appropriate software.
2. Electric field due to the uniform electric field (same as before):
E_uniform = 4900 N/C
To calculate the net electric field at x = +0.19 m, we again add the electric field due to the point charge and the electric field due to the uniform electric field:
E_net_x_plus = E_uniform + E_point_location
Calculate the sum of these two quantities to find the net electric field at x = +0.19 m.
(c) y = +0.19 m:
Since the uniform electric field is directed only in the x-direction, the y-component of the net electric field will be zero at all points. Therefore, the magnitude of the net electric field at y = +0.19 m will be zero.
Remember to use appropriate units throughout the calculations and pay attention to the signs of charges and electric field components.