A charged sphere of mass m=1kg and charge q=2*10^-4 C is attached to a non-condu

Question

A charged sphere of mass m=1kg and charge q=2*10^-4 C is attached to a non-conducting long string. It is deflected from its equilibrium position through an angle 30degrees as shown in the region of uniform electric field E=-3*10^4i V/m as shown. Find the tension in the string as the sphere passes its equilibrium position. (Question15 in the picture)

A charged sphere of mass m = 1.0 kg and charge q = 2.0 times 10-4 C is attached to a non - conducting long string. It is deflected from its equilibrium position through an angle phi = 30 degree as shown in the region of uniform electric field E = - 3.0 times 104i V/m as shown. Find the tension in the string as the sphere passes its equilibrium position.

Explanation / Answer

conserving energy,

all the P.E is converted to K.E and potential energy stored in the electric field

So, mgl*cosQ = 0.5*mv^2-Eql*sinQ

So, v = sqrt((mgl*cosQ+Eql*sinQ)*2/m)

so,

T - mg = mv^2/l

So, T = mg + mv^2/l = mg+ m*(mgl*cosQ+Eql*sinQ)*2/ml

= mg + 2*(mg*cosQ+Eq*sinQ)

= 1*9.8 + 2*(1*9.8*cos(30 degrees)+3*10^4*2*10^-4*sin(30 degrees))

= 32.77 N <---------------answer

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