A 3.0 mC point charge is placed in an external uniform electric field of 1.6×10^4 N/C. At what distance from the charge is the net electric field zero?

Calculate how far from the point charge the E field from that charge has magnitude of 1.6*10^4 N/C

1.3m

To determine the distance from the charge where the net electric field is zero, we can use the formula for electric field due to a point charge:

E = k * Q / r^2

Where:
E is the electric field
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
Q is the charge magnitude
r is the distance from the charge

In this case, we have:
Q = 3.0 mC (3.0 x 10^-3 C)
E = 1.6 x 10^4 N/C

Setting the electric field to zero, we can rearrange the formula:

0 = k * Q / r^2

Rearranging to solve for r:

r^2 = k * Q / 0

r^2 = ∞

Since the electric field formula does not yield an actual value for r, it implies that the electric field will never be exactly zero if the charge is present.

However, in practical situations, the electric field becomes negligible at a very large distance from the charge. Hence, the actual distance at which the electric field is almost zero can be considered to be at infinity.

To find the distance from the point charge where the net electric field is zero, we can use the concept of superposition, which states that the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.

In this case, there is only one charge, so the net electric field is solely due to the external uniform electric field and will be zero at some distance from the charge.

The formula to calculate the electric field produced by a uniform electric field is:

E = Q / (4πε₀r²),

where E is the electric field, Q is the charge, ε₀ is the permittivity of free space, and r is the distance from the charge.

In this case, the external uniform electric field is given as 1.6×10^4 N/C. We need to find the distance (r) when the net electric field is zero.

To solve for r, we can set the electric field produced by the external field equal to zero:

0 = Q / (4πε₀r²).

Since the charge Q is given as 3.0 mC (3.0 × 10^-3 C), we substitute these values into the equation:

0 = (3.0 × 10^-3 C) / (4πε₀r²).

Now we solve for r by rearranging the equation:

r² = (3.0 × 10^-3 C) / (4πε₀ × 0).

Since ε₀ is a constant (8.854 × 10^-12 C²/Nm²), and we have divided by zero, the net electric field can only be zero if the charge is at an infinite distance. In other words, there is no finite distance at which the net electric field will be zero with this external electric field.