The figure below shows two point charges, 𝑄1 = +7.50 nC and 𝑄2 = −8.30 nC, separated bya distance of 5.00 mm.Calculate(a) the force acted upon 𝑄1.(b) the electric field strength at the centre between the point charges.(c) the electric potential at the centre between the point charges.
Question
The figure below shows two point charges, 𝑄1 = +7.50 nC and 𝑄2 = −8.30 nC, separated bya distance of 5.00 mm.Calculate(a) the force acted upon 𝑄1.(b) the electric field strength at the centre between the point charges.(c) the electric potential at the centre between the point charges.
Solution
(a) To calculate the force acted upon Q1, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is:
F = k * |Q1*Q2| / r^2
where:
- F is the force,
- k is Coulomb's constant (8.99 * 10^9 N m^2/C^2),
- Q1 and Q2 are the charges (in Coulombs), and
- r is the distance between the charges (in meters).
First, we need to convert the charges from nC to C by multiplying by 10^-9. So, Q1 = 7.50 * 10^-9 C and Q2 = -8.30 * 10^-9 C. The distance also needs to be converted from mm to m, so r = 5.00 * 10^-3 m.
Substituting these values into the formula gives:
F = 8.99 * 10^9 * |(7.50 * 10^-9) * (-8.30 * 10^-9)| / (5.00 * 10^-3)^2
Solving this will give the force in Newtons.
(b) The electric field strength at a point due to a charge is given by the formula:
E = k * |Q| / r^2
where:
- E is the electric field strength,
- Q is the charge creating the field, and
- r is the distance from the charge to the point.
The total electric field at the center between the charges will be the vector sum of the fields due to each charge. Since the charges are of opposite sign and the same distance from the center, their fields will be in opposite directions and can be subtracted.
E_total = E_Q1 - E_Q2
Substitute the values for Q1, Q2, and r into the formula and solve to find the electric field strength.
(c) The electric potential at a point due to a charge is given by the formula:
V = k * Q / r
where:
- V is the electric potential,
- Q is the charge creating the potential, and
- r is the distance from the charge to the point.
The total electric potential at the center between the charges will be the sum of the potentials due to each charge, since electric potential is a scalar quantity.
V_total = V_Q1 + V_Q2
Substitute the values for Q1, Q2, and r into the formula and solve to find the electric potential.
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