Chapter 29, Problem 29.8OQ

Classify each of die following statements as a characteristic (a) of electric forces only, (b) of magnetic forces only, (c) of both electric and magnetic forces, or (d) of neither electric nor magnetic forces. (i) The force is proportional to the magnitude of the field exerting it. (ii) The force is proportional to the magnitude of the charge of the object on which the force is exerted. (iii) The force exerted on a negatively charged object is opposite in direction to the force on a positive charge. (iv) The force exerted on a stationary charged object is nonzero. (v) The force exerted on a moving charged object is zero. (vi) The force exerted on a charged object is proportional to its speed. (vii) The force exerted on a charged object cannot alter the object’s speed. (viii) The magnitude of the force depends on the charged object’s direction of motion.

To determine

The forces which are proportional to the magnitude of their respective fields.

Answer to Problem 29.8OQ

Option(c) of both electric and magnetic forces.

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

Here,

$F_{\text{e}}$ is the force on the particle due to electric field.

$q$ is the magnitude of charge on the particle.

$E$ is the magnitude of electric field intensity.

Increase the electric field, the force on the charge will also increase proportional to it.

$F_{\text{e}}\propto E$

The expression for magnetic force is,

$F_{\text{m}}=qvB\sin \theta$

Here,

$F_{\text{m}}$ is the force on the particle due to magnetic field.

$q$ is the magnitude of charge on the particle.

$B$ is the magnitude of magnetic flux density.

$\theta$ is the angle between the motion of the particle and the magnetic field line.

Increase the magnetic field with same speed on same charge in the same direction, the force on the charge will also increase proportional to it.

$F_{\text{m}}\propto B$

Conclusion:

The electric force is proportional to the electric field and the magnetic force is proportional to the magnetic field. Both electric and magnetic forces are proportional to their respective fields but option (a) includes only electric force. Thus, option (a) is incorrect.

The magnetic force is proportional to the magnetic field and the electric force is proportional to the electric field. Both the forces are proportional to their respective fields but option (b) includes only magnetic force. Thus, option (b) is incorrect.

Both the forces are proportional to their respective fields. Thus option (c) is correct.

The exerted forces in magnetic field as well as electric field are proportional to their respective field that contradicts the option (d). Thus, option (d) is incorrect.

To determine

The forces proportional to the magnitude of the charge.

Answer to Problem 29.8OQ

Option (c) both electric and magnetic forces

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

Increase the magnitude of charge, the force on the charge will also increase proportional to it.

$F_{\text{e}}\propto q$

The expression for magnetic force is

$F_{\text{m}}=qvB\sin \theta$

Increase the magnitude of charge with same speed and in the same field, in the same direction, the force on the charge will also increase proportional to it.

$F_{\text{m}}\propto q$

Conclusion:

The electric force is proportional to the magnitude of charge and the magnetic force is also proportional to magnitude of charge. Both electric and magnetic forces are proportional to the magnitude of charge but option (a) includes only electric force. Thus, option (a) is incorrect.

The magnetic force is proportional to the magnitude of charge and also the electric force is proportional to magnitude of charge .Both the forces are proportional to the magnitude of charge but option (b) only magnetic force. Thus, option (b) is incorrect.

Both the forces are proportional to the magnitude of charge. Thus option (c) is correct.

The exerted forces in magnetic field as well as electric field are proportional to the magnitude of charge that contradicts the option (d). Thus, option (d) is incorrect.

To determine

The forces which exert force on a negatively charged particle in opposite direction to the force on a positively charged particle.

Answer to Problem 29.8OQ

Option (c) both electric and magnetic forces.

Explanation of Solution

The electric force on a positively charged particle is

${\overrightarrow{F}}_{{\text{e}}^{+}}=+q\overrightarrow{E}$ (1)

Here

${\overrightarrow{F}}_{{\text{e}}^{+}}$ is the electric force vector on the positively charged particle.

$q$ is the magnitude of charge on the particle.

$\overrightarrow{E}$ is the electric field intensity.

The electric force on a negatively charged particle is

${\overrightarrow{F}}_{{\text{e}}^{-}}=-q\overrightarrow{E}$ (2)

Here

${\overrightarrow{F}}_{{\text{e}}^{-}}$ is the electric force vector on the positively charged particle.

From equation (1) and equation (2),

${\overrightarrow{F}}_{{\text{e}}^{+}}=-{\overrightarrow{F}}_{{\text{e}}^{-}}$

Thus, electric force on the same magnitude of electric charge of opposite nature are equal but opposite in direction.

The magnetic force on a positively charged particle is,

${\overrightarrow{F}}_{{\text{m}}^{+}}=+q\left(\overrightarrow{v}\otimes \overrightarrow{B}\right)$ (3)

Here

${\overrightarrow{F}}_{{\text{m}}^{+}}$ is the magnetic force vector on the positively charged particle.

$q$ is the magnitude of charge on the particle.

$\overrightarrow{B}$ is the electric flux density.

$v$ is the speed of the particle.

The magnetic force on a negatively charged particle is,

${\overrightarrow{F}}_{{\text{m}}^{-}}=-q\left(\overrightarrow{v}\otimes \overrightarrow{B}\right)$ (4)

Here,

${\overrightarrow{F}}_{{\text{m}}^{-}}$ is the electric force vector on the positively charged particle.

From equation (3) and (4),

${\overrightarrow{F}}_{{\text{m}}^{+}}={\overrightarrow{-F}}_{{\text{m}}^{-}}$

Thus, magnetic force on the same magnitude of electric charge moving with same speed but of opposite nature are equal but opposite in direction.

Conclusion:

Both magnetic force and electric force exert force on negative charge in the opposite direction to the force on positive charge but option (a) includes only electric force. Thus, option (a) is incorrect.

Both magnetic force and electric force exert force on negative charge in the opposite direction to the force on positive charge but option (b) includes only magnetic force. Thus option (b) is incorrect.

Both magnetic force and electric force exert force on negative charge in the opposite direction to the force on positive charge. Thus, option (c) is correct.

Both the forces exert force on negative charge in the opposite direction to the force on positive charge that contradicts the option (d). Thus, option (d) is incorrect.

To determine

The forces which are non-zero on a stationary object.

Answer to Problem 29.8OQ

Option (a) only electric forces exert non-zero force on stationary object.

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

There is no relation between motion of charged object and electric field because electric field exists for all orientations of charges, whether it is stationary or in motion.

The expression for magnetic force is,

$F_{\text{m}}=qvB\sin \theta$

Magnetic force exists only when charges are in motion. Thus for stationary charges the magnetic force is not valid.

Conclusion:

Electrical force is valid for any particle that has charge; it is fundamental force in nature. Thus, option (a) is correct.

Magnetic field is existence for any charged particle in motion. Stationary charged particles have zero magnetic force. Thus option (b) is incorrect.

For a stationary charge only electric force is non-zero and magnetic force is zero that contradicts the option (c). Thus, option (c) is incorrect.

For a stationary charge only electric force is non-zero and magnetic field is zero which is contradictory to the option (d). Thus, option (d) is incorrect.

To determine

The forces which are zero on a moving charge.

Answer to Problem 29.8OQ

Option (d) neither electric nor magnetic force.

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

There is no relation between motion of charged object and electric field because electric field exists for all orientations of charges, whether it is stationary or in motion. If electric field exists then there is a non-zero force on the charged object.

The expression for magnetic force is,

$F_{\text{m}}=qvB\sin \theta$

Magnetic force exists only when charges are in motion. Thus for moving charges the magnetic force may be zero if the charge moves either in the direction of the magnetic field or opposite to it.

Conclusion:

Electrical force is valid for any particle that has charge; it is fundamental force in nature. Thus, option (a) is incorrect.

Magnetic field is existence for any charged object in motion. Moving charged objects may have zero magnetic force if the charged object moves along or against the direction of the magnetic field. Thus, option (b) is incorrect.

For a moving charge, electric force is non-zero but the magnetic force may or may not be zero that contradicts the option (c). Thus, option (c) is incorrect.

For a moving charge only electric force is non-zero and magnetic force may or may not be zero. Thus option (d) is correct.

To determine

The forces proportional to the speed of the charged object.

Answer to Problem 29.8OQ

option (b) magnetic forces only.

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

There is no relation between motion of charged object and the electric field force.

The expression for magnetic force is,

$F_{\text{m}}=qvB\sin \theta$

The magnetic force exists only if there is motion and is directly proportional to the speed of the charged particle.

$F_{\text{m}}\propto v$

Conclusion:

The electric force exerted on the charged object has no relation with its motion. Thus option (a) is incorrect.

The magnetic force is exerted on a body in motion and is directly proportional to the speed of the object. Thus option (b) is correct.

The electric force exerted on the charged object has no relation with its motion while magnetic force on it is proportional to the speed of the object. Thus, option (c) is incorrect.

The electric force exerted on the charged object has no relation with its motion while magnetic force on it is proportional to the speed of the object that contradicts the option (d). Thus, option (d) is incorrect.

To determine

The forces on the charged object which can alter its speed.

Answer to Problem 29.8OQ

Option (b) magnetic forces only.

Explanation of Solution

The expression for electrical force is,

$F_{\text{e}}=qE$

There is no relation between motion of charged object and the electric field force.

The expression for magnetic force is,

$\overrightarrow{F_{\text{m}}}=q\left(\overrightarrow{v}\otimes \overrightarrow{B}\right)$

The magnetic force acts on the perpendicular direction of the motion of the object because it is along the direction of cross product vector of $\overrightarrow{v}$ and $\overrightarrow{B}$. The force does not change the magnitude of the velocity but it changes the direction of motion.

Conclusion:

There is no relation of motion of the charged object and the electric field force. Thus option (a) is incorrect.

The magnetic force has no change in the speed but it does change the direction of motion of the object. Thus option (b) is correct.

Electric forces have no relation with speed of the charged body while magnetic forces cannot alter speed of the object but it can change its direction of motion. Thus option (c) is incorrect.

Electric forces are independent of any motion of the charged object while magnetic forces can change only the direction of motion of the object. Thus option (d) is incorrect

To determine

The force whose magnitude depends on the charged object’s direction of motion.

Answer to Problem 29.8OQ

Option (b) magnetic forces only

Explanation of Solution

The expression for electrical force is

$F_{\text{e}}=qE$

There is no relation between motion of charged object and the electric field force.

The expression for magnetic force is

$F_{\text{m}}=qvB\sin \theta$

The value of $\theta$ depends upon the direction of motion of the charged object Change in the direction of motion changes value of $\theta$ and so the magnetic force varies.

Conclusion:

The electric field has no relation with the motion of the charged object Thus option (a) is incorrect.

The variation in direction of motion varies the value of $\theta$ which in turn varies the value of the magnitude of magnetic force. Thus option (b) is correct.

The direction of motion of the charged object affects only the magnetic force but not electric force. Thus option (c) is incorrect as it considers both the forces.

Only the magnetic force is affected by variation in direction of motion of the charged object but not electric force. Thus option (d) is incorrect as it considers neither of the forces.