A point particle moves with uniform angular velocity on a circular pathA5]centred on the origin, and is acted on by the field:rdrF(r) = -K-dtin which k and b are positive constants, r is the position vector of the particle (withmagnitude r) and t is a parameter.x = a cos t, y = a sin t, (0 < t < 27), find an expression for the field in terms of t anddetermine the work done during a single circuit of the particle. Hence state acondition for F(r) to be conservative.Using the standard parameterisation,

Solution: The position vector of the particle is r and can be converted into the function of t, as…

A5] A point particle moves with uniform angular velocity on a circular path centred on the origin, and is acted on by the field: r F(r) = -K- dr b dt in which K and b are positive constants, r is the position vector of the particle (with magnitude r) and t is a parameter. Using the standard parameterisation, x = a cost, y = a sint, (0 ≤ t ≤ 2π), find an expression for the field in terms of t and determine the work done during a single circuit of the particle. Hence state a condition for F(r) to be conservative.

A5] A point particle moves with uniform angular velocity on a circular path centred on the origin, and is acted on by the field: r F(r) = -K- dr b dt in which K and b are positive constants, r is the position vector of the particle (with magnitude r) and t is a parameter. Using the standard parameterisation, x = a cost, y = a sint, (0 ≤ t ≤ 2π), find an expression for the field in terms of t and determine the work done during a single circuit of the particle. Hence state a condition for F(r) to be conservative.