Question

what formula gives the strength of an electric field, e, at a distance from a known source charge?
○ ( e = \frac{f_e}{qd} )
○ ( e = \frac{kq}{d} )
○ ( e = \frac{kq}{d^2} )
○ ( e = \frac{f_e}{d} )

Explanation:

To determine the formula for the electric field strength \( E \) from a source charge, we recall the definition and derivation:

1. The electric field \( E \) is defined as the electric force \( F_e \) per unit test charge \( q \), so \( E = \frac{F_e}{q} \) (but this is a general definition, not specific to distance from a source charge).
2. For a point source charge \( q \), Coulomb’s law gives the force \( F_e = \frac{kq q_{\text{test}}}{d^2} \), where \( k \) is Coulomb’s constant, \( q \) is the source charge, \( q_{\text{test}} \) is the test charge, and \( d \) is the distance. Dividing \( F_e \) by \( q_{\text{test}} \) (to get force per unit test charge) gives \( E = \frac{kq}{d^2} \).

Now, analyze the options:

• \( E = \frac{F_e}{qd} \): Incorrect (includes an extra \( d \) not in the definition).
• \( E = \frac{kq}{d} \): Incorrect (distance should be squared, as electric field follows an inverse - square law).
• \( E = \frac{kq}{d^2} \): Correct (matches the derivation for the electric field from a point charge).
• \( E = \frac{F_e}{d} \): Incorrect (does not align with the definition of electric field or Coulomb’s law).

Answer:

\( \boldsymbol{E = \frac{kq}{d^2}} \) (the third option, e.g., if options are labeled as A, B, C, D: C. \( E = \frac{kq}{d^2} \))