Hang on the Charged particle

Electricity and Magnetism Level 1

The above is a particle with $-q$ of electric charge, hanging on a string in the horizontally uniform electric filed. The mass of the charged particle is $m$ and the hanging angle of the string to the vertical line is $30$ °. What is the electric field strength? (Ignore the mass of the string.)

\frac{\sqrt{3}mg}{3q}

\frac{mg}{q}

\frac{mg}{2}

\frac{\sqrt{2}mg}{2q}

1 solution

Karen Adelan
Mar 9, 2014

just show me the right solution, i just guess it :)

due the electric field,there is a electric force acting on the particle having charge=-q(it's magnitude=qEand it's direction is oppsite to the direction of electric field)......................and mg is acting downward,,,now draw the free-body diagram of the particle..........................in the f.b.d,the angle b/w the mg and resultant of mg and qE is 30 deg. ..then using tan 30=qE/mg...................... we get....E=mg/((sqrt 3)*q)....... multiplying by (sqrt 3) in denominator as well as in numerator....... we get the answer......

Naveen Chandra - 7 years, 2 months ago

there is Tension in the string. The magnitude of vertical component of tension in string = wight (mg) & the horizontal component must be equal to force due to electric field. (as charge is stationary no net force should act on it). You shold calculate the horizontal component in order to work out the electric field strength. to calculate it you can make a vector triangle & by simple trigonometric ratio you can calculate the horizontal component (tan 30 * mg). As now you know the force due to electric field (F) on the charge (q) (i.e horizontal component) you can simply calculate electric field strength by formula: E=F/q.

Faraz Burni - 7 years, 2 months ago

Hang on the Charged particle

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