Solve

Guides

Polar Representation of a Complex Number

Question

A uniform electric field having strenght is existing in x-y plane as shown in figure. Find the p.d. between origin O & A (d,d,0),

A

E d (c o s θ + s i n θ)

B

- E d (s i n θ - c o s θ)

C

\sqrt{2} E d

D

None of these

Open in App

Solution

Verified by Toppr

When the electric field E in x-y plane makes angle $θ$ with the x-axis , the electric filed can be written as $\to E = E cos θ^i + E sin θ^j$
Thus, $E_{x} = E cos θ$ , $E_{y} = E sin θ$ and $E_{z} = 0$
Since $\to E = - \frac{\to \nabla V}{d r}$
So, $d V_{x} = - E_{x} d x$ , $d V_{y} = - E_{y} d y$ and $d V_{z} = - E_{z} d z$
Now ingratiating, $V_{x} = - \int_{d}^{0} E cos θ d x = - E cos θ (0 - d) = E d cos θ$
$V_{y} = - \int_{d}^{0} E sin θ d y = - E sin θ (0 - d) = E d sin θ$
and $V_{z} = 0$
Thus, potential between O and A is $V = V_{x} + V_{y} + V_{z} = E d cos θ + E d sin θ$

Was this answer helpful?

0

Similar Questions

Q1

The electric field in a region surrounding the origin is uniform and along the x-axis. A small circle is drawn with the centre at the origin cutting the axes at points B, C, and D having co-ordinates (a, 0), (0, a), (– a, 0), (0, – a); respectively as shown in figure.Potential will be maximum at the point?

View Solution

Q2

$(c o s e c θ - c o t θ)^{2}$ = ?

(a) $\frac{1 + c o s θ}{1 - c o s θ}$ (b) $\frac{1 - c o s θ}{1 + c o s θ}$ (c) $\frac{1 + s i n θ}{1 - s i n θ}$ (d) none of these

View Solution

Q3

The electric field in a region surrounding the origin is uniform and along the x-axis. A small circle is drawn with the centre at the origin cutting the axes at points B, C, and D having co-ordinates (a, 0), (0, a), (– a, 0), (0, – a); respectively as shown in figure.Potential will be maximum at the point?

View Solution

Q4

A short dipole is placed at origin of coordinate system in $x-y$ plane as shown in figure. Find the electric field at point $P (0, y)$ . $(y >>$ length of dipole $)$

View Solution

Q5

The uniform electric field in a region surrounding the origin is along the $x -$ axis. A small circle is drawn with the center at the origin cutting the axes at points $A, B, C$ and $D$ having coordinates $(a, 0), (0, a), (- a, 0)$ and $(0, - a)$ respectively, as shown in figure. Find the point at which the potential is minimum.

View Solution

Solve

Guides