Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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.
Consider a system of n charges q1, q2, ... qn with position vectors `vecr_1,vecr_2,vecr_3,...... vecr_n`relative to some origin 'O'. Deduce the expression for the net electric field`vec E` at a point P with position vector `vecr_p,`due to this system of charges.
Can a gravitational field be added vectorially to an electric field to get a total field?
In some old texts it is mentioned that 4π lines of force originate from each unit positive charge. Comment on the statement in view of the fact that 4π is not an integer.
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.
Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.
A particle of mass 1 g and charge 2.5 × 10−4 C is released from rest in an electric field of 1.2 × 10 4 N C−1. What will be the speed of the particle after travelling this distance?
A particle of mass 1 g and charge 2.5 × 10−4 C is released from rest in an electric field of 1.2 × 10 4 N C−1. How much is the work done by the electric force on the particle during this period?
12 J of work has to be done against an existing electric field to take a charge of 0.01 C from A to B. How much is the potential difference VB − VA?
The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the center of the disc is `sigma/(2∈_0)`. With respect to the field at the center, the electric field along the axis at a distance R from the center of the disc ______.
Consider a region inside which, there are various types of charges but the total charge is zero. At points outside the region ______.
When 1014 electrons are removed from a neutral metal sphere, the charge on the sphere becomes ______.
The Electric field at a point is ______.
- always continuous.
- continuous if there is no charge at that point.
- discontinuous only if there is a negative charge at that point.
- discontinuous if there is a charge at that point.
