PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 16, Problem 110P

(a)

To determine

The net electric force acting on the dipole.

(a)

Expert Solution
Check Mark

Answer to Problem 110P

The net force is 0N.

Explanation of Solution

The charges of dipole are ±3.0μC, separation between charges is 7.0cm, electric field is 2.0×104N/C, mass of charge is 5.0g, and the mass of rod is 20.0g.

Write the equation to find the x-component of net force.

Fx=qExqEx

Here, Fx is the x-component of net force, q is the magnitude of charge, and Ex is the x-component of electric field.

The first terms on the right hand side of above equation denotes x-component of force due to positive charge and the second terms denotes the x-component of force due to negative charge on the dipole.

Rewrite the above relation.

Fx=0N

Write the equation to find the y-component of net force.

Fy=qEyqEy

Here, Fy is the y-component of net force and Ey is the y-component of electric field.

The first terms on the right hand side of above equation denotes y-component of force due to positive charge and the second terms denotes the y-component of force due to negative charge on the dipole.

Rewrite the above relation.

Fy=0N

Write the equation for net electric force.

Fnet=(Fx)2+(Fy)2

Here, Fnet is the net electric force.

Conclusion:

Substitute 0N for Fx and Fy in the above equation to find Fnet.

Fnet=(0N)2+(0N)2=0N

Therefore, the net force is 0N.

(b)

To determine

Prove that the magnitude of torque on the dipole is τ=qEdsinθ.

(b)

Expert Solution
Check Mark

Answer to Problem 110P

It is proved that the magnitude of torque on the dipole is τ=qEdsinθ.

Explanation of Solution

The charges of dipole are ±3.0μC, separation between charges is 7.0cm, electric field is 2.0×104N/C, mass of charge is 5.0g, and the mass of rod is 20.0g.

Write the equation for net torque.

τ=Fqrqsinθ+Fqrqsinθ

Here, τ is the net torque, Fq is the force due to negative charge, rq is the moment arm of negative charge (half of the separation between the charges), Fq is the force due to positive charge, rq is the moment arm of negative charge (half of the separation between the charges), and θ is the angle made by dipole with the electric field.

Write the equation for Fq.

Fq=qE

Write the equation for Fq.

Fq=qE

Write the equation for rq.

rq=d2

Here, d is the separation between charges.

Write the equation for rq.

rq=d2

Rewrite the equation for τ by substituting the above relations for rq.

τ=qE(d2)sinθ+qE(d2)sinθ=qEdsinθ (I)

Conclusion:

Therefore, it is proved that the magnitude of torque on the dipole is τ=qEdsinθ.

(c)

To determine

Torque acting on the dipoles at angles θ=0°,36.9°,90.0°

(c)

Expert Solution
Check Mark

Answer to Problem 110P

Torques at angles θ=0°,36.9°,90.0° are 0Nm, 0.0025Nm,and0.0042Nm respectively.

Explanation of Solution

The charges of dipole are ±3.0μC, separation between charges is 7.0cm, electric field is 2.0×104N/C, mass of charge is 5.0g, and the mass of rod is 20.0g.

Conclusion:

Substitute 3.0μC for q, 2.0×104N/C for E, 7.0cm for d, and 0° for θ in equation (I) to find τ.

τ=(3.0μC(106C1μC))(2.0×104N/C)(7.0cm(102m1cm))(sin0°)=(42×104Nm)(0)=0Nm

Substitute 3.0μC for q, 2.0×104N/C for E, 7.0cm for d, and 90.0° for θ in equation (I) to find τ.

PHYSICS, Chapter 16, Problem 110P

Substitute 3.0μC for q, 2.0×104N/C for E, 7.0cm for d, and 90.0° for θ in equation (I) to find τ.

τ=(3.0μC(106C1μC))(2.0×104N/C)(7.0cm(102cm1cm))(sin90.0°)=(42×104Nm)(1.0)=0.0042Nm

Therefore, torques at angles θ=0°,36.9°,90.0° are 0Nm, 0.0025Nm,and0.0042Nm respectively.

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Chapter 16 Solutions

PHYSICS

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