Electric Charges And Fields

Question

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A rigid insulated wire frame in the form of a right-angled triangle ABC, is set in a vertical plane as shown in fig. Two beads of equal masses m each and carrying charges q₁and q₂ are connected by a cord of length l and can slide without friction on the wires.
Considering the case when the beads are stationary, determine
(i) the angle $α$
(ii) the tension in the cord and
(iii) the normal reaction on the beads.
If the cord is now cut, what are the values of the charges for which the beads continue to remain stationary?

Solution

The forces acting on the bead P are shown in the figure below.

charge on beads are q₁and q₂length of the cord = l
Assuming that the charges are similar, the repulsive force F is

F = k \frac{q_{1} q_{2}}{l^{2}}

where, K is a constant.

Let T be the tension in the string and N₁be the normal reaction on the bead at P.
Considering the components of forces perpendicular and parallel to AB we have, for equilibrium,

mg \cos 60 ° = (T - F) \cos α

...(i)

N_{1} = mg \cos 30 ° + (T - F) \sin α

...(ii)

For the bead at

θ

, we have

mg \sin 60 ° = (T - F) \sin α

...(iii)

N_{2} = mg \cos 60 ° + (T - F) \cos α

...(iv)

Squaring and adding equation (i) and (iii) we get

m^{2} g^{2} = (T - F)^{2}

T - F = \pm mg

...(v)

Assuming that the charges are similar, we have

T - F = + mg

T = F + mg = k \frac{q_{1} q_{2}}{l^{2}} + mg

...(vi)

From equation (i) we have

mg \cos 60 ° = mg \cos α

∴

α = 60 °

Equation (ii) gives

N_{1} = mg [\cos 30 ° + \cos 30 °] = mg \cos 30 ° + mg \sin 60 ° = 2 mg \cos 30 ° = mg \sqrt{3}

From equation (iv) we have

N_{2} = mg \cos 60 ° + mg \cos 60 ° = mg

If the string is cut, T = 0 and we get, from equation (v)

F = \pm mg F = k \frac{q_{1} q_{2}}{l^{2}} = \pm mg

\Rightarrow

q_{1} q_{2} = \frac{\pm mg l^{2}}{k}

Thus q₁ and q₂ may have same or opposite signs to remain stationary.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?