4. A charge of 10-10 C is placed at the corner of an equilateral triangle of side 3 cm. What is the Amount of work must be done to make this possible (a) 3.0 x 10-9 (b) 4.5×109/ (c) 9.0x 109 (d) 10.0 × 10°/
The amount of work done to bring a charge from infinity to a point is given by the formula:
W = qV
Where:
W = Work done
q = Charge
V = Electric potential at the location of the charge
Given that the charge q = 10^-10 C and it is placed at a corner of an equilateral triangle of side 3 cm. The electric potential at a point due to a charge q at a distance r is given by:
V = kq/r
Where:
k = Coulomb's constant = 8.99 x 10^9 Nm^2/C^2
r = distance from the charge q
Since the triangle is equilateral, the distance from the corner to the center of the triangle will be 3/√3 = √3 cm.
Therefore, the electric potential at the corner where the charge is placed will be:
V = (8.99 x 10^9 Nm^2/C^2)(10^-10 C)/√3
Now, we can find the amount of work done:
W = (10^-10 C)((8.99 x 10^9 Nm^2/C^2)(10^-10 C)/√3)
W = 8.99 x 10^-1 Nm^2/√3
W ≈ 4.5 x 10^-1 Nm^2
Therefore, the amount of work done to make this possible is approximately 4.5 x 10^-1 Nm^2.
Therefore, the answer is (b) 4.5 x 10^-1.