A point charge is placed at the origin an x, y coordinate grid. Then, a curve is drawn to connect all the points in the xy plane where the electric field has magnitude 1.0 N/C. What best describes the curve?
A. a wide loop that passes through the origin
B. a circle centered at the origin
C. a straight line of infinite length through the origin
D. a straight line of finite length that doesn't pass through the origin
(My guess is that the answer is either C or D.)
wrong !
We want force on a unit charge at distance R
think about Force = constant / R^2
what is the geometry with a constant radius R ??? !!!
To determine the best description of the curve in the xy plane where the electric field has a magnitude of 1.0 N/C, let's refer to the formula for electric field magnitude:
Electric field magnitude (E) = k * (Q / r^2)
Where:
- k is the Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2)
- Q is the charge of the point charge at the origin
- r is the distance from the point charge
Since the electric field magnitude is constant at 1.0 N/C, we can set up the equation:
1.0 N/C = k * (Q / r^2)
Since we are only concerned with the shape of the curve and not the specific values, we can ignore the constants. Thus the equation becomes:
1 = Q / r^2
To analyze the above equation, let's consider different values for Q and r:
1. When Q = 1 C, the equation simplifies to:
1 = 1 / r^2
r^2 = 1
r = ±1
2. When Q = 2 C, the equation simplifies to:
1 = 2 / r^2
r^2 = 2
r ≈ ±1.414
Based on the above calculations, we observe that the curve is circular in shape, centered at the origin, and passes through the points (±1, 0) and (0, ±1). Therefore, the best description of the curve is option B: a circle centered at the origin.
To determine which option is correct, we need to understand the properties of the electric field generated by a point charge. The electric field magnitude produced by a point charge decreases with the square of the distance from the charge.
In this case, we have a point charge located at the origin. The field magnitude decreases as we move away from the origin. We are looking for points in the xy plane where the electric field has a magnitude of 1 N/C.
Option A suggests a wide loop passing through the origin. This is unlikely because the electric field would need to be symmetrically distributed around the origin at all distances for the loop to be closed. However, the electric field from a point charge does not exhibit this behavior.
Option B proposes a circle centered at the origin. This is the correct option. As we move away from the origin, the electric field magnitude decreases. Points at a certain distance from the origin will have an electric field magnitude of 1 N/C. Therefore, the curve connecting all these points will indeed form a circle centered at the origin.
Option C suggests a straight line of infinite length through the origin. This doesn't match the behavior of the electric field produced by a point charge.
Option D proposes a straight line of finite length that doesn't pass through the origin. This also doesn't match the behavior of the electric field from a point charge since the electric field decreases with distance from the origin.
Therefore, the correct answer is B: a circle centered at the origin.