Which one of the following is NOT a property of equipotential surface?
No work is done in moving a test charge from one point to another on an equipotential surface.
The electric field is always perpendicular to an equipotential surface.
None of the above
The direction of the equipotential surface is from low potential to high potential.
Two equipotential surfaces can never intersect.
The direction of the equipotential surface is from low potential to high potential.
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
The torque on an electric dipole in a uniform electric field is given by the formula:
τ = pE sinθ
where τ is the torque, p is the magnitude of the dipole moment, E is the magnitude of the electric field, and θ is the angle between the dipole moment and the electric field.
In this case, we are given E = 10^5 N/C and the distance between the charges is 0.12 m. The magnitude of the dipole moment is given by:
p = qd
where q is the charge and d is the separation between the charges.
Using q = 1.6 x 10^-19 C and d = 0.12 m, we can calculate the magnitude of the dipole moment:
p = (1.6 x 10^-19 C)(0.12 m) = 1.92 x 10^-20 C·m
The angle between the dipole moment and the electric field is 90 degrees since they are parallel to each other.
Now we can substitute the values into the formula for torque:
τ = (1.92 x 10^-20 C·m)(10^5 N/C)(sin 90°)
Since sin 90° = 1, the torque simplifies to:
τ = 1.92 x 10^-20 C·m·N
Therefore, the magnitude of the torque is 1.92 x 10^-20 C·m·N.
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 magnitude of the torque on an electric dipole in a uniform electric field is given by the formula:
τ = pE sinθ
where τ is the torque, p is the magnitude of the dipole moment, E is the magnitude of the electric field, and θ is the angle between the dipole moment and the electric field.
In this case, we are given E = 10^5 N/C and the distance between the charges is 0.12 m. The magnitude of the dipole moment is given by:
p = qd
where q is the charge and d is the separation between the charges.
Using q = 1.6 x 10^-19 C and d = 0.12 m, we can calculate the magnitude of the dipole moment:
p = (1.6 x 10^-19 C)(0.12 m) = 1.92 x 10^-20 C·m
The angle between the dipole moment and the electric field is 90 degrees since they are parallel to each other.
Now we can substitute the values into the formula for torque:
τ = (1.92 x 10^-20 C·m)(10^5 N/C)(sin 90°)
Since sin 90° = 1, the torque simplifies to:
τ = 1.92 x 10^-15 N·m
Therefore, the magnitude of the torque is 1.92 x 10^-15 N·m.
The property that is NOT a property of an equipotential surface is:
The direction of the equipotential surface is from low potential to high potential.
To determine which one of the given options is NOT a property of an equipotential surface, let's analyze each option:
1. No work is done in moving a test charge from one point to another on an equipotential surface.
This property is indeed a characteristic of an equipotential surface. When a test charge is moved along an equipotential surface, there is no change in potential energy, hence no work is done.
2. The electric field is always perpendicular to an equipotential surface.
This is also a property of an equipotential surface. The electric field lines are always perpendicular to the equipotential surfaces at each point. This means that no component of the electric field is parallel to the equipotential surface.
3. None of the above.
This option does not provide any specific characteristic of an equipotential surface, so it cannot be considered as the correct answer.
4. The direction of the equipotential surface is from low potential to high potential.
This is also a property of an equipotential surface. The direction of the equipotential surface is always from regions of lower potential to regions of higher potential.
5. Two equipotential surfaces can never intersect.
This statement is NOT a property of an equipotential surface. In reality, equipotential surfaces can intersect each other. The intersection occurs when the potentials at two different points are equal.
Therefore, the correct answer is:
Two equipotential surfaces can never intersect.