the charges an coodinates of two points charges located in x-y palne are : q1=+3*10^-6 C ; x=+3.5 cm . y=+0,5 cm and q2=-4*10^

-6 C; x= - 2 cm y=+1.5 cm . (a)Find the electric potential at the origin(b)How much work must be done to locate these charges at their given positions ,

starting from infinity?

To find the electric potential at the origin and the work required to locate the charges, we can use the formulas for electric potential and electrostatic potential energy.

(a) Electric potential at the origin (V):
The electric potential at a point in space is given by the formula V = k * (q / r), where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point.

For q1:
Charge (q1) = +3 * 10^-6 C
Distance (r1) = √(x1^2 + y1^2) = √((0.035 m)^2 + (0.005 m)^2) = √(0.001225 + 0.000025) = √0.00125 ≈ 0.0354 m

Substituting these values into the electric potential formula, we have:
V1 = (9 x 10^9 Nm^2/C^2) * (+3 * 10^-6 C) / (0.0354 m)
V1 ≈ 76.3 V

For q2:
Charge (q2) = -4 * 10^-6 C
Distance (r2) = √(x2^2 + y2^2) = √((-0.02 m)^2 + (0.015 m)^2) = √(0.0004 + 0.000225) = √0.000625 ≈ 0.025 m

Substituting these values into the electric potential formula, we have:
V2 = (9 x 10^9 Nm^2/C^2) * (-4 * 10^-6 C) / (0.025 m)
V2 ≈ -2.88 V

Thus, the electric potential at the origin is the sum of V1 and V2:
Electric potential at the origin = V1 + V2 ≈ 73.4 V

(b) Work required to locate the charges at their positions from infinity:
The work done to move a charge from infinity to a given position is equal to the change in its electrostatic potential energy (U).

The formula for electrostatic potential energy is U = k * (q1 * q2) / r, where k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.

For the given setup, the work done is equal to the sum of the work required to move q1 and q2 individually.

For q1:
Charge (q1) = +3 * 10^-6 C
Distance (r1) = √(x1^2 + y1^2) = √((0.035 m)^2 + (0.005 m)^2) = √0.001225 ≈ 0.0354 m
Calculating the work done for q1:
W1 = k * [(q1 * q_infinity) / r1] = k * [(q1 * 0) / r1] = 0

Similarly, for q2:
Charge (q2) = -4 * 10^-6 C
Distance (r2) = √(x2^2 + y2^2) = √((-0.02 m)^2 + (0.015 m)^2) = √0.0004 ≈ 0.020 m
Calculating the work done for q2:
W2 = k * [(q2 * q_infinity) / r2] = k * [(q2 * 0) / r2] = 0

Hence, the total work done to locate the charges at their given positions, starting from infinity, is zero.