Four charges are placed on corners of a square as shown in figure having side of 5,cm . If Q is one

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1. Electric Charges and Fields

hard

Four charges are placed on corners of a square as shown in figure having side of $5\,cm$. If $Q$ is one microcoulomb, then electric field intensity at centre will be

$1.02 \times {10^7}N/C$ upwards

$2.04 \times {10^7}N/C$ downwards

$2.04 \times {10^7}N/C$ upwards

$1.02 \times {10^7}N/C$ downwards

Solution

(a) Side $a = 5 \times 10^{-2} m$
Half of the diagonal of the square $r = \frac{a}{{\sqrt 2 }}$
Electric field at centre due to charge q $E = \frac{{kq}}{{{{\left( {\frac{a}{{\sqrt 2 }}} \right)}^2}}}$
Now field at O $ = \sqrt {{E^2} + {E^2}} = E\sqrt 2 $$ = \frac{{kq}}{{{{\left( {\frac{a}{{\sqrt 2 }}} \right)}^2}}}.\sqrt 2 $
$ = \frac{{9 \times {{10}^9} \times {{10}^{ – 6}} \times \sqrt 2 \times 2}}{{{{(5 \times {{10}^{ – 2}})}^2}}}$$ = 1.02 \times {10^7}\,N/C$ (upward)

Standard 12

Physics

Two point charges $Q_1, Q_2$ are fixed at $x = 0$ and $x = a$. Assuming that field strength is positive in the direction coinciding with the positive direction of $x$, then, which following option will be correct ?

hard

A charged ball $B$ hangs from a silk thread $S$, which makes an angle $\theta $ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma $ of the sheet is proportional to

medium

(AIEEE-2005)

The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is

medium

(JEE MAIN-2022)

Select the correct statement : (Only force on a particle is due to electric field)

easy

What is the magnitude of a point charge which produces an electric field of $2\, N/coulomb$ at a distance of $60\, cm$ $(1/4\pi {\varepsilon _0} = 9 \times {10^9}\,N – {m^2}/{C^2})$