Figure below shows an electric dipole in a uniform electric field with magnitude 10 cross times 10 to the power of 5 N/C directed parallel to the plane of the figure.The electric dipole consists of two charges q subscript 1 equals plus e and q subscript 2 equals negative e space left parenthesis e equals 1.6 cross times 10 to the power of negative 19 end exponent right parenthesis, which both lie in the plane and separated by a distance 0.12 space n text m end text
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Calculate the magnitude of the torque
The magnitude of the torque (τ) on an electric dipole in a uniform electric field can be calculated using the formula:
τ = p * E * sin(θ)
Where:
p = dipole moment = q * d
q = charge on each constituent of the dipole = 1.6 x 10^-19 C
d = distance between the charges of the dipole = 0.12 m
E = electric field strength = 10^5 N/C (given)
θ = angle between the dipole moment vector and the electric field vector
In this case, the dipole moment vector is in the plane of the figure and perpendicular to the electric field vector, so the angle (θ) is 90 degrees (π/2 radians).
Using the given values:
q = 1.6 x 10^-19 C
d = 0.12 m
E = 10^5 N/C
θ = 90 degrees (π/2 radians)
p = q * d = (1.6 x 10^-19 C) * (0.12 m) = 1.92 x 10^-20 Cm
τ = p * E * sin(θ) = (1.92 x 10^-20 Cm) * (10^5 N/C) * sin(π/2) = 1.92 x 10^-15 Nm
Therefore, the magnitude of the torque on the electric dipole is 1.92 x 10^-15 Nm.
To calculate the magnitude of the torque on an electric dipole in a uniform electric field, we can use the formula:
Torque = p * E * sin(theta)
Where:
- p is the magnitude of the dipole moment
- E is the magnitude of the electric field
- theta is the angle between the dipole moment and the electric field
Given:
- Electric field magnitude (E) = 10^5 N/C
- Both charges (q1 and q2) have a magnitude of e = 1.6 * 10^-19 C
- Distance between charges (d) = 0.12 nm = 0.12 * 10^-9 m
First, let's calculate the dipole moment (p):
p = q * d
Where:
- q is the charge magnitude of either one of the charges (q1 or q2)
- d is the distance between the charges
p = (1.6 * 10^-19 C) * (0.12 * 10^-9 m)
p = 1.92 * 10^-28 C*m
Next, let's find the angle (theta) between the dipole moment and the electric field. Since the electric field is parallel to the plane of the figure, the angle theta is 0 degrees. However, the sin(0) = 0, so the torque would be zero. Therefore, the torque on the dipole in this case is zero.
To calculate the magnitude of the torque acting on the electric dipole, we can use the equation:
Torque = magnitude of electric field x dipole moment x sin(theta)
Here, the magnitude of the electric field given is 10 * 10^5 N/C (10 times 10 to the power of 5 N/C).
The dipole moment can be calculated using the formula:
dipole moment = charge magnitude (q) x separation distance (d)
In this case, the charges are q1 = +e and q2 = -e, where e = 1.6 * 10^-19 C, and the separation distance is 0.12 nm (which can be converted to meters by dividing by 10^9).
Plugging these values into the formula, the dipole moment is:
dipole moment = (q1 x d) - (q2 x d)
= (1.6 * 10^-19 C * 0.12 * 10^-9 m) - (-1.6 * 10^-19 C * 0.12 * 10^-9 m)
Now we can calculate the magnitude of the torque:
Torque = (10 * 10^5 N/C) * (1.6 * 10^-19 C * 0.12 * 10^-9 m) * sin(theta)
Note that theta is the angle between the direction of the electric field and the dipole moment. Since the electric field is directed parallel to the plane of the figure, the angle theta is 90 degrees.
Therefore,
Torque = (10 * 10^5 N/C) * (1.6 * 10^-19 C * 0.12 * 10^-9 m) * sin(90°)
Solving this equation will give you the magnitude of the torque acting on the electric dipole.