Particle A of charge 2.76 10-4 C is at the origin, particle B of charge -6.54 10-4 C is at (4.00 m, 0), and particle C of charge 1.02 10-4 C is at (0, 3.00 m). We wish to find the net electric force on C.
(a) What is the x component of the electric force exerted by A on C?
(b) What is the y component of the force exerted by A on C?
(c) Find the magnitude of the force exerted by B on C.
(d) Calculate the x component of the force exerted by B on C.
(e) Calculate the y component of the force exerted by B on C.
(f) Sum the two x components from parts (a) and (d) to obtain the resultant x component of the electric force acting on C.
(g) Similarly, find the y component of the resultant force vector acting on C.
(h) Find the magnitude and direction of the resultant electric force acting on C.
magnitude? N
direction? ° counterclockwise from the +x-axis
To find the net electric force on particle C, we need to calculate the individual forces exerted by particles A and B on C and then combine them.
(a) The x component of the electric force exerted by particle A on C can be calculated using Coulomb's Law:
Electric force = (k * |q1 * q2|) / r^2
where k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between the particles. Since particle A is at the origin, the distance (r) between A and C is 3.00 m.
Substituting the values into the formula:
Electric force exerted by A on C = (8.99 x 10^9 N m^2/C^2) * (|2.76 x 10^-4 C| * |1.02 x 10^-4 C|) / (3.00 m)^2
Calculate the above expression to find the x component of the electric force exerted by A on C.
(b) The y component of the force exerted by particle A on C can be found similarly to part (a), just with the y components of the charges and distances.
(c) The magnitude of the force exerted by particle B on C can be calculated using Coulomb's Law in the same way as part (a), but using the charge and distance values for particle B and C.
(d) The x component of the force exerted by particle B on C can be found similarly to part (a), just with the x components of the charges and distances.
(e) The y component of the force exerted by particle B on C can be found similarly to part (d), just with the y components of the charges and distances.
(f) To find the resultant x component of the electric force acting on C, simply sum the x components of the forces exerted by particles A and B, calculated in parts (a) and (d) respectively.
(g) Similarly, to find the resultant y component of the electric force acting on C, sum the y components of the forces exerted by particles A and B, calculated in parts (b) and (e) respectively.
(h) To find the magnitude of the resultant electric force acting on C, use the Pythagorean theorem:
Magnitude = sqrt((resultant x component)^2 + (resultant y component)^2)
To find the direction, use the inverse tangent function:
Direction = atan(resultant y component / resultant x component)
This will give you the direction in radians. To convert it to degrees, multiply by 180/π.
Note: When using Coulomb's Law, be careful with the signs and directions of the charges to ensure the correct direction of forces.