Advertisements
Advertisements
प्रश्न
A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of −2 × 10−9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).
Advertisements
उत्तर
Charge located at the origin, q = 8 mC = 8 × 10−3 C
Magnitude of a small charge, which is taken from a point P to point R to point Q, q1 = −2 × 10−9 C
All the points are represented in the given figure.
Point P is at a distance, d1 = 3 cm, from the origin along the z-axis.
Point Q is at a distance, d2 = 4 cm, from the origin along the y-axis.
Potential at point P, `"V"_1 = "q"/(4piin_0 xx "d"_1)`
Potential at point Q,`"V"_2 = "q"/(4piin_0 xx "d"_2)`
Work done (W) by the electrostatic force is independent of the path.
∴ `"W" = "q"_1 ["V"_2 - "V"_1]`
= `"q"_1["q"/(4piin_0"d"_2) - "q"/(4piin_0"d"_1)]`
= `("qq"_1)/(4piin_0) [1/"d"_2 - 1/"d"_1]` .......(1)
Where, `1/(4piin_0) = 9 xx 10^9 "N m"^2 "C"^-2`
∴ `"W" = 9 xx 10^9 xx 8 xx 10^-3 xx (-2 xx 10^-9)[1/0.04 - 1/0.03]`
= `-144 xx 10^-3 xx ((-25)/3)`
= 1.27 J
Therefore, work done during the process is 1.27 J.
APPEARS IN
संबंधित प्रश्न
Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).
Work done by a uniform electric field 'E' in moving a charge 'q' at a distance 'd' from a to b is ______.
Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B.
 |
 |
 |
| (i) | (ii) | (iii) |
Depict the orientation of an electric dipole in (a) stable and (b) unstable equilibrium in an external uniform electric field. Write the potential energy of the dipole in each case.
Under what condition is the torque on a dipole in a uniform electric field non-zero?
What is the formula for torque acting on a dipole making an angle θ with a uniform electric field?
In vector form, how is the torque on a dipole expressed in terms of dipole moment and electric field?
What must an external agent do to rotate a dipole slowly in a uniform electric field?
What reference angle is chosen to simplify the potential energy formula for a dipole, and why?
What is the final formula for the potential energy of a dipole in a uniform electric field?
What is the relationship between the torque direction and the direction of dipole rotation?
How does the potential energy of a dipole change as it rotates from being antiparallel (θ = 180°) to being parallel (θ = 0°) with the electric field?
If the electric field strength is doubled while keeping the dipole orientation constant, how does the potential energy change?
