Two charges of −4𝜇𝐶 and +4𝜇𝐶 are placed at the points A(1, 0, 4)m and B(2, -1, 5)m located inan electric field⃗ 𝐸 = 0.10̂ 𝑖 𝑉 /𝑐𝑚. Find the torque acting on the dipole
Question
Two charges of −4𝜇𝐶 and +4𝜇𝐶 are placed at the points A(1, 0, 4)m and B(2, -1, 5)m located inan electric field⃗ 𝐸 = 0.10̂ 𝑖 𝑉 /𝑐𝑚. Find the torque acting on the dipole
Solution
The torque acting on an electric dipole in an electric field is given by the formula:
τ = p x E
where p is the dipole moment and E is the electric field.
Step 1: Calculate the dipole moment (p)
The dipole moment is given by the formula:
p = q * d
where q is the charge and d is the distance between the charges.
Given that the charges are -4μC and +4μC, and the coordinates of the charges are A(1, 0, 4)m and B(2, -1, 5)m, we can calculate the distance between the charges using the formula for the distance between two points in 3D space:
d = sqrt[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²]
Substituting the given coordinates:
d = sqrt[(2 - 1)² + (-1 - 0)² + (5 - 4)²] = sqrt[1 + 1 + 1] = sqrt[3] m
Therefore, the dipole moment is:
p = q * d = 4μC * sqrt[3] m = 4sqrt[3] μC.m
Step 2: Calculate the torque (τ)
The electric field E is given as 0.1 i V/cm. We need to convert this to V/m by multiplying by 100, so E = 10 i V/m.
The torque is then given by:
τ = p x E = 4sqrt[3] μC.m * 10 i V/m = 40sqrt[3] μC.V
Therefore, the torque acting on the dipole is 40sqrt[3] μC.V.
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