Advertisements
Advertisements
प्रश्न
An electric field \[\vec{E} = \vec{i}\] Ax exists in space, where A = 10 V m−2. Take the potential at (10 m, 20 m) to be zero. Find the potential at the origin.
Advertisements
उत्तर
Given:
Electric field intensity,
\[\vec{E} = \hat{ i } \text{Ax} = 10\text{ x } \hat{i} \]
Potential,
\[dV = - \vec{E} . \vec{\text{dx}} = - 10\text{xdx}\]
On integrating, we get
\[V = 10 \times \frac{x^2}{2} = - \left[ 5 x^2 \right]_{10}^0 \]
\[V = 5 \times 100 = 500 \] V
So, at the origin, the potential is 500 V.
APPEARS IN
संबंधित प्रश्न
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
Show that if we connect the smaller and the outer sphere by a wire, the charge q on the former will always flow to the latter, independent of how large the charge Q is.
The charge on a proton is +1.6 × 10−19 C and that on an electron is −1.6 × 10−19 C. Does it mean that the electron has 3.2 × 10−19 C less charge than the proton?
When the separation between two charges is increased, the electric potential energy of the charges
The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin, cutting the axes at points A, B, C and D with coordinates (a, 0), (0, a), (−a, 0), (0, −a), respectively. Out of the points on the periphery of the circle, the potential is minimum at
Consider the situation in the figure. The work done in taking a point charge from P to Ais WA, from P to B is WB and from P to C is WC.
Electric potential decreases uniformly from 120 V to 80 V, as one moves on the x-axis from x = −1 cm to x = +1 cm. The electric field at the origin
(a) must be equal to 20 Vcm−1
(b) may be equal to 20 Vcm−1
(c) may be greater than 20 Vcm−1
(d) may be less than 20 Vcm−1
Which of the following quantities does not depend on the choice of zero potential or zero potential energy?
Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.
A wire is bent in the form of a regular hexagon and a total charge q is distributed uniformly on it. What is the electric field at the centre? You may answer this part without making any numerical calculations.
A ball of mass 100 g and with a charge of 4.9 × 10−5 C is released from rest in a region where a horizontal electric field of 2.0 × 104 N C−1 exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball? (c) Where will the ball be at the end of 2 s?
Consider the situation of the previous problem. A charge of −2.0 × 10−4 C is moved from point A to point B. Find the change in electrical potential energy UB − UA for the cases (a), (b) and (c).
Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire of mass 6.4 g (take the atomic weight of copper to be 64 g mol−1).
Which of the following methods can be used to charge a metal sphere positively without touching it? Select the most appropriate.
Two identical blocks are kept on a frictionless horizontal table connected by a spring of stiffness k and of original length l0. A total charge Q is distributed on the block such that maximum elongation of spring at equilibrium is equal to x. Value of Q is ______.
In general, metallic ropes are suspended on the carriers taking inflammable materials. The reason is ______.
When 1014 electrons are removed from a neutral metal sphere, the charge on the sphere becomes ______.
The electric field intensity produced by the radiations coming from 100 W bulb at 3 m distance is E. The electric field intensity produced by the radiations coming from 50 W bulb at the same distance is:
