Charged particles q1=− 4.80 nC and q2=+ 4.80 nC are separated by distance 3.00 mm , forming an electric dipole. The charges are in a uniform electric field whose direction makes an angle 36.4° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude 8.00×10^−9 N⋅m ?

Respuesta :

Answer:

Electric field, E = 936.19 N/C

Explanation:

It is given that,

Charge 1, [tex]q_1=-4.8\ nC=-4.8\times 10^{-9}\ C[/tex]

Charge 2, [tex]q_2=+4.8\ nC=+4.8\times 10^{-9}\ C[/tex]

Distance between them, d = 3 mm = 0.003 m

Torque, [tex]\tau=8\times 10^{-9}\ N-m[/tex]

Angle between electric field and line connecting the charge, [tex]\theta=36.4^{\circ}[/tex]

We need to find the torque exerted on the dipole. The torque experienced by the dipole in the electric field is given by :

[tex]\tau=pE\ sin\theta[/tex]

p is the dipole moment, [tex]p=qd[/tex]

[tex]\tau=qdE\ sin\theta[/tex]

[tex]E=\dfrac{\tau}{qd\ sin\theta}[/tex]

[tex]E=\dfrac{8\times 10^{-9}}{4.8\times 10^{-9}\times 0.003\ sin(36.4)}[/tex]

E = 936.19 N/C

So, the magnitude of electric field on the dipole is 936.19 N/C. Hence, this is the required solution.