a charge 5mc is placed at a point. What is the work required to carry 1C of charge once round it in a circle of radius 12cm.
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To find the work required to carry 1C of charge once round a charged particle, we can use the formula for the electric potential energy difference.
The formula for electric potential energy is given by:
PE = q * V
Where:
PE is the electric potential energy
q is the charge
V is the electric potential (also known as voltage)
In this case, we need to find the work done, which is the change in electric potential energy when carrying the additional 1C charge around the original charge.
Since the charge is positive, it will create a positive potential difference, resulting in positive work done.
To find the electric potential at a point due to a point charge, we use the formula:
V = k * (q / r)
Where:
V is the electric potential
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q is the charge of the point charge
r is the distance between the point charge and the point where the potential is being measured
In this case, the charge is 5mc (milli-coulombs), which can be expressed as 5 * 10^(-3) C (Coulombs). The radius of the circle is given as 12cm, which can be converted to meters by dividing by 100: 12cm / 100 = 0.12m.
Now we can calculate the electric potential at this distance from the charge:
V = (9 x 10^9 Nm^2/C^2) * (5 * 10^(-3) C) / 0.12 m
Simplifying the expression:
V = 3750000 Nm/C
The work done to carry a charge around the charged particle is equal to the change in electric potential energy. Since we are adding 1C of charge, the change in electric potential energy is given by:
ΔPE = q * ΔV = 1 C * (3750000 Nm/C) = 3750000 Nm
Therefore, the work required to carry 1C of charge once round the charged particle in a circle of radius 12cm is 3750000 Nm.