12. 12.1 A charge of \( -5 \times 10^{-9} \mathrm{C} \) is placed in an electrical field where the electrical field strength is \( 8 \times 10^{3} \) \( \mathrm{~N} \cdot \mathrm{C}^{-1} \) downwards. Calculate the force that is exerted on the charge by the electrical field.

1. We start with the formula for the electrical force on a charge: \[ F = qE \] 2. Here, the charge is given by: \[ q = -5 \times 10^{-9} \, \mathrm{C} \] and the electric field strength is: \[ E = 8 \times 10^{3} \, \mathrm{N \cdot C^{-1}} \] 3. Substitute these values into the formula: \[ F = \left(-5 \times 10^{-9}\right) \times \left(8 \times 10^{3}\right) \] 4. Multiply the numerical coefficients and the powers of ten separately: \[ -5 \times 8 = -40 \quad \text{and} \quad 10^{-9} \times 10^{3} = 10^{-6} \] Therefore: \[ F = -40 \times 10^{-6} \, \mathrm{N} \] 5. Simplify the expression: \[ -40 \times 10^{-6} \, \mathrm{N} = -4 \times 10^{-5} \, \mathrm{N} \] 6. The negative sign indicates that the force is in the direction opposite to the direction of the electric field; since the field is downward, the force on the negative charge is upward. The final answer is: \[ F = -4 \times 10^{-5} \, \mathrm{N} \]