At a certain distance from a point charge, the electric field is 500 V/m and the potential is 3000 V. What is the distance?

• A: 6 m
• B: 12 m
• C: 36 m
• D: 144 m

To find the distance from a point charge given the electric field and potential, we can use the formulas for electric field (E) and electric potential (V). The electric field due to a point charge is given by:

Formulas to Use

• E = k * |Q| / r² (Electric Field)
• V = k * Q / r (Electric Potential)

Here, k is Coulomb's constant (approximately 8.99 x 10⁹ N m²/C²), Q is the charge, and r is the distance from the charge.

Relating Electric Field and Potential

The relationship between electric field and potential is:

E = -dV/dr, which implies that:

V = E * r when considering a uniform field.

Calculating the Distance

From the given values:

• Electric Field, E = 500 V/m
• Potential, V = 3000 V

Using the formula for potential:

3000 V = 500 V/m * r

Now, solve for r:

r = 3000 V / 500 V/m = 6 m

Final Answer

The distance from the point charge is 6 m, which corresponds to option A.