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
q6.png
Calculate the magnitude of the torque
1.92 cross times 10 to the power of negative 29 end exponent space text Nm end text
None of the above
1.23 cross times 10 to the power of negative 23 end exponent space text Nm end text
0 space text Nm end text
1.32 cross times 10 to the power of negative 33 end exponent space text Nm end text
The torque experienced by an electric dipole in a uniform electric field can be calculated using the formula:
τ = pE sinθ
where:
τ = torque
p = dipole moment (p = qd)
E = magnitude of the electric field
θ = angle between the dipole moment vector and the electric field vector
In this case, the dipole moment is given by p = qd, where q is the charge and d is the separation distance between the charges. We are given the values of q and d, so we can calculate the dipole moment:
p = (1.6 x 10^-19 C)(0.12 m) = 1.92 x 10^-20 C*m
We are also given the magnitude of the electric field, which is 10^5 N/C.
Now, let's calculate the angle θ. Since the electric field is directed parallel to the plane of the figure, the dipole moment vector will be perpendicular to the electric field vector, hence θ = 90 degrees.
sinθ = sin 90° = 1
Finally, let's calculate the torque:
τ = (1.92 x 10^-20 C*m)(10^5 N/C)(1) = 1.92 x 10^-15 N*m
Therefore, the magnitude of the torque is 1.92 x 10^-15 Nm.
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
q6.png
Calculate the magnitude of the torque
1.92 cross times 10 to the power of negative 29 end exponent space text Nm end text
None of the above
1.23 cross times 10 to the power of negative 23 end exponent space text Nm end text
0 space text Nm end text
1.32 cross times 10 to the power of negative 33 end exponent space text Nm end text
To calculate the magnitude of the torque, we need to use the formula τ = pEsinθ, where τ is the torque, p is the dipole moment, E is the magnitude of the electric field, and θ is the angle between the dipole moment and the electric field.
Given:
q1 = +e = +1.6 x 10^-19 C
q2 = -e = -1.6 x 10^-19 C
d = 0.12 m
E = 10^5 N/C
The dipole moment, p, can be calculated as the product of one of the charges and the separation distance:
p = q1d = (1.6 x 10^-19 C)(0.12 m) = 1.92 x 10^-20 C·m
The angle between the dipole moment and electric field is 0 degrees, as they are parallel in this case.
Now, let's calculate the torque:
τ = pEsinθ = (1.92 x 10^-20 C·m)(10^5 N/C)(sin 0°) = 0 N·m
Therefore, the magnitude of the torque is 0 Nm.
Which of the following is a vector?
None of the above
Electric field
Electric potential energy
Electric potential
Equipotential lines
The electric field is a vector.
To calculate the magnitude of the torque, we can use the formula:
Torque = p * E * sin(theta),
where p is the electric dipole moment, E is the magnitude of the electric field, and theta is the angle between the dipole moment and the electric field.
The electric dipole moment, p, is given by the formula:
p = q * d,
where q is the charge magnitude and d is the separation between the charges.
Given:
q1 = +e = +1.6 * 10^-19 C,
q2 = -e = -1.6 * 10^-19 C,
d = 0.12 * 10^-3 m,
E = 10^5 N/C.
First, let's calculate the electric dipole moment:
p = q * d
= (+1.6 * 10^-19 C) * (0.12 * 10^-3 m)
= 1.92 * 10^-22 Cm
Next, let's calculate the angle theta. Since the electric field is parallel to the plane of the figure, the dipole moment is also parallel. Therefore, the angle theta is 0 degrees or 180 degrees.
Now, let's calculate the magnitude of the torque using the formula:
Torque = p * E * sin(theta)
Since sin(0) = 0, the torque will be 0 Nm.
Therefore, the correct answer is:
0 Nm.
To calculate the magnitude of the torque on an electric dipole in a uniform electric field, you can use the formula:
Torque = electric field strength * dipole moment * sinθ
1. First, calculate the dipole moment. The dipole moment is the product of the magnitude of one of the charges and the separation between the charges.
Dipole moment = q * d
where q is the magnitude of one charge and d is the separation between the charges.
Dipole moment = (1.6 x 10^-19 C) * (0.12 m)
2. Next, determine the angle between the electric field and the dipole moment. In this case, the electric field is parallel to the plane of the figure, so the angle θ between the electric field and the dipole moment is 0 degrees.
3. Now, you can calculate the torque using the formula:
Torque = (electric field strength) * (dipole moment) * sinθ
Given that the electric field strength is 10^5 N/C, the dipole moment is (1.6 x 10^-19 C) * (0.12 m), and sinθ is sin(0) = 0, the torque is:
Torque = (10^5 N/C) * (1.6 x 10^-19 C) * (0) = 0 Nm
Therefore, the correct answer is 0 Nm.