# Electric Field and minimum velocity

• erisedk
In summary, the equation 1/2 mv^2 = QΔV is used to calculate the minimum velocity needed for a small ring with mass M and charge +Q to reach the other end of a smooth non-conducting rod, given an electric field E = E0/l (xi + yj) N/C in the xy plane. By integrating the force of the electric field over the entire path of the ring, the solution yields a minimum velocity of zero. However, integrating until the point of highest potential, (l/2, l/2), yields a non-zero minimum velocity.
erisedk

## Homework Statement

Electric field given by the vector E = E0/l (xi + yj) N/C is present in the xy plane. A small ring of mass M carrying charge +Q, which can slide freely on a smooth non-conducting rod, is projected along the rod from the point (0,l) such that it can reach the other end of the rod at (l,0) . Assuming there is no gravity in the region, what minimum velocity should be given to the ring, if QE0l/M = 8

## The Attempt at a Solution

1/2 mv^2 = QΔV
dV = E.ds (ds is the displacement)
dV ={ E0/l (xi + yj) } {dx i + dy j}
= E0/l (xdx + ydy)
V = E0/l ∫xdx + ∫ydy ( ∫xdx from 0 to l, ∫ydy from l to 0)
= 0

Hence velocity required is zero.
Which is terribly wrong.

Look (visually) at the field xi+yj maybe you will get some insight as to why the answer came out to be zero.

Edit:
What is the minimum velocity needed to get over a hill?
By analogy, your method is to integrate the force of gravity (dot ds) over the entire hill.
But of course, this yields an answer of zero (if the hill is the same height on both sides).

Last edited:
Got this one, just had to integrate till the point of highest potential, i.e. (l/2, l/2).
Thanks :)

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence that a charged particle has on other charged particles in its vicinity. It is represented by a vector and is measured in units of volts per meter (V/m).

## 2. How is an electric field created?

An electric field is created by a charged object, such as an electron or a proton. This charged object exerts a force on other charged particles in its surroundings, creating an electric field.

## 3. What is the minimum velocity required for a charged particle to experience an electric field?

The minimum velocity required for a charged particle to experience an electric field is zero. As long as the charged particle has a charge, it will experience an electric field, regardless of its velocity.

## 4. How does the strength of an electric field affect the motion of a charged particle?

The strength of an electric field directly affects the acceleration of a charged particle. The stronger the electric field, the greater the acceleration of the charged particle.

## 5. What is the relationship between electric field and minimum velocity?

There is no direct relationship between electric field and minimum velocity. The minimum velocity required for a charged particle to experience an electric field depends on the strength of the electric field and the charge of the particle.

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