A charged particle is whirled in a horizontal circle on a frictionless table by attaching it to a string fixed at one point. If a magnetic field is switched on in the vertical direction, how will it affect the tension in the string?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → It may increase or decrease
The tension in the string supplies the centripetal force \( mv^{2}/r \). A vertical field adds the magnetic force \( q\vec{v}\times\vec{B} \). This force is perpendicular to both \( \vec{v} \) and \( \vec{B} \). So it acts along the string, towards the centre or away from it. This force does no work, so the speed and the required centripetal force stay the same.
Option (1) It will increase — Incorrect. The tension rises only when the magnetic force points away from the centre. If the field is reversed, or the charge has the opposite sign, the force points inward and the tension falls.
Option (2) It will decrease — Incorrect. The tension falls only when the magnetic force points towards the centre. If the field is reversed, or the particle goes round the other way, the force points outward and the tension rises.
Option (3) It will remain the same — Incorrect. The velocity is horizontal and the field vertical, so the magnetic force \( qvB \) is not zero and changes the force the string must supply.
Option (4) It may increase or decrease — Correct. The direction of \( q\vec{v}\times\vec{B} \) depends on the sign of the charge, the sense of rotation and whether the field points up or down. The question does not give any of these.
Force towards the centre: \( T=mv^{2}/r-qvB \), so the tension decreases.
Force away from the centre: \( T=mv^{2}/r+qvB \), so the tension increases.
NCERT (2026-27):
Magnetic Field, Lorentz Force – “(ii) The magnetic force q [ v × B ] includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.”
Motion in a Magnetic Field – “… In the case of motion of a charge in a magnetic field, the magnetic force is perpendicular to the velocity of the particle. So no work is done and no change in the magnitude of the velocity is produced (though the direction of momentum may be changed).”